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Journal articles on the topic 'Fixed point argument'

Author: Grafiati

Published: 7 August 2022

Last updated: 8 August 2022

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1

Khan, Abdul Qadeer. "Global Dynamics, Bifurcation Analysis, and Chaos in a Discrete Kolmogorov Model with Piecewise-Constant Argument." Mathematical Problems in Engineering 2021 (November 5, 2021): 1–14. http://dx.doi.org/10.1155/2021/5259226.

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The local behavior with topological classifications, bifurcation analysis, chaos control, boundedness, and global attractivity of the discrete-time Kolmogorov model with piecewise-constant argument are investigated. It is explored that Kolmogorov model has trivial and two semitrival fixed points for all involved parameters, but it has an interior fixed point under definite parametric condition. Then, by linear stability theory, local dynamics with different topological classifications are investigated around trivial, semitrival, and interior fixed points. Further for the discrete Kolmogorov model, existence of periodic points is also investigated. It is also investigated the occurrence of bifurcations at interior fixed point and proved that at interior fixed point, there exists no bifurcation, except flip bifurcation by bifurcation theory. Next, feedback control method is utilized to stabilize chaos existing in discrete Kolmogorov model. Boundedness and global attractivity of the discrete Kolmogorov model are also investigated. Finally, obtained results are numerically verified.

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2

Jachymski, Jacek. "Another proof of the Browder–Göhde–Kirk theorem via ordering argument." Bulletin of the Australian Mathematical Society 65, no. 1 (February 2002): 105–7. http://dx.doi.org/10.1017/s0004972700020104.

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Using the Zermelo Principle, we establish a common fixed point theorem for two progressive mappings on a partially ordered set. This result yields the Browder–Göhde–Kirk fixed point theorem for nonexpansive mappings.

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3

Došlá, Zuzana, Mauro Marini, and Serena Matucci. "A fixed-point approach for decaying solutions of difference equations." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2191 (January 4, 2021): 20190374. http://dx.doi.org/10.1098/rsta.2019.0374.

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A boundary value problem associated with the difference equation with advanced argument * Δ ( a n Φ ( Δ x n ) ) + b n Φ ( x n + p ) = 0 , n ≥ 1 is presented, where Φ ( u ) = | u | α sgn u , α > 0, p is a positive integer and the sequences a , b , are positive. We deal with a particular type of decaying solution of (*), that is the so-called intermediate solution (see below for the definition). In particular, we prove the existence of this type of solution for (*) by reducing it to a suitable boundary value problem associated with a difference equation without deviating argument. Our approach is based on a fixed-point result for difference equations, which originates from existing ones stated in the continuous case. Some examples and suggestions for future research complete the paper. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

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4

Guezane-Lakoud, A., and R. Khaldi. "Multiple Positive Solutions for a Fractional Boundary Value Problem with Fractional Integral Deviating Argument." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/651508.

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This work is devoted to the existence of positive solutions for a fractional boundary value problem with fractional integral deviating argument. The proofs of the main results are based on Guo-Krasnoselskii fixed point theorem and Avery and Peterson fixed point theorem. Two examples are given to illustrate the obtained results, ending the paper.

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5

Jaradat, Mohammed M. M., Babak Mohammadi, Vahid Parvaneh, Hassen Aydi, and Zead Mustafa. "PPF-Dependent Fixed Point Results for Multi-Valued ϕ-F-Contractions in Banach Spaces and Applications." Symmetry 11, no. 11 (November 6, 2019): 1375. http://dx.doi.org/10.3390/sym11111375.

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The solutions for many real life problems is obtained by interpreting the given problem mathematically in the form of f ( x ) = x . One of such examples is that of the famous Borsuk–Ulam theorem, in which using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this paper, we initiate ϕ − F -contractions and study the existence of PPF-dependent fixed points (fixed points for mappings having variant domains and ranges) for these related mappings in the Razumikhin class. Our theorems extend and improve the results of Hammad and De La Sen [Mathematics, 2019, 7, 52]. As applications of our PPF dependent fixed point results, we study the existence of solutions for delay differential equations (DDEs) which have numerous applications in population dynamics, bioscience problems and control engineering.

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6

Premoselli, Bruno. "A pointwise finite-dimensional reduction method for a fully coupled system of Einstein–Lichnerowicz type." Communications in Contemporary Mathematics 20, no. 06 (August 27, 2018): 1750076. http://dx.doi.org/10.1142/s0219199717500766.

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We construct non-compactness examples for the fully coupled Einstein–Lichnerowicz constraint system in the focusing case. The construction is obtained by combining pointwise a priori asymptotic analysis techniques, finite-dimensional reductions and a fixed-point argument. More precisely, we perform a fixed-point procedure on the remainders of the expected blow-up decomposition. The argument consists of an involved finite-dimensional reduction coupled with a ping-pong method. To overcome the non-variational structure of the system, we work with remainders which belong to strong function spaces and not merely to energy spaces. Performing both the ping-pong argument and the finite-dimensional reduction therefore heavily relies on the a priori pointwise asymptotic techniques of the [Formula: see text] theory.

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7

O'Regan, Donal. "Existence results for differential equations with reflection of the argument." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 57, no. 2 (October 1994): 237–60. http://dx.doi.org/10.1017/s1446788700037538.

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AbstractExistence principles are given for systems of differential equations with reflection of the argument. These are derived using fixed point analysis, specifically the Nonlinear Alternative. Then existence results are deduced for certain classes of first and second order equations with reflection of the argument.

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8

Brattka, Vasco, Stéphane Le Roux, Joseph S. Miller, and Arno Pauly. "Connected choice and the Brouwer fixed point theorem." Journal of Mathematical Logic 19, no. 01 (June 2019): 1950004. http://dx.doi.org/10.1142/s0219061319500041.

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We study the computational content of the Brouwer Fixed Point Theorem in the Weihrauch lattice. Connected choice is the operation that finds a point in a non-empty connected closed set given by negative information. One of our main results is that for any fixed dimension the Brouwer Fixed Point Theorem of that dimension is computably equivalent to connected choice of the Euclidean unit cube of the same dimension. Another main result is that connected choice is complete for dimension greater than or equal to two in the sense that it is computably equivalent to Weak Kőnig’s Lemma. While we can present two independent proofs for dimension three and upward that are either based on a simple geometric construction or a combinatorial argument, the proof for dimension two is based on a more involved inverse limit construction. The connected choice operation in dimension one is known to be equivalent to the Intermediate Value Theorem; we prove that this problem is not idempotent in contrast to the case of dimension two and upward. We also prove that Lipschitz continuity with Lipschitz constants strictly larger than one does not simplify finding fixed points. Finally, we prove that finding a connectedness component of a closed subset of the Euclidean unit cube of any dimension greater than or equal to one is equivalent to Weak Kőnig’s Lemma. In order to describe these results, we introduce a representation of closed subsets of the unit cube by trees of rational complexes.

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9

CHARKI, Z. "THE INITIAL VALUE PROBLEM FOR THE DEEP BÉNARD CONVECTION EQUATIONS WITH DATA IN Lq." Mathematical Models and Methods in Applied Sciences 06, no. 02 (March 1996): 269–77. http://dx.doi.org/10.1142/s0218202596000584.

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10

Ait Dads, Elhadi, Samir Fatajou, and Lahcen Khachimi. "Pseudo Almost Automorphic Solutions for Differential Equations Involving Reflection of the Argument." ISRN Mathematical Analysis 2012 (September 20, 2012): 1–20. http://dx.doi.org/10.5402/2012/626490.

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By means of the fixed point methods and the properties of the pseudo almost automorphic functions, the existence and uniqueness of pseudo almost automorphic solutions are obtained for differential equations involving reflection of the argument. For the nonscalar, case we use the exponential dichotomy properties.

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11

Wu, Li, and Chuanzhi Bai. "Application of Fixed-Point Index Theory for a Nonlinear Fractional Boundary Value Problem with an Advanced Argument." Discrete Dynamics in Nature and Society 2021 (September 23, 2021): 1–7. http://dx.doi.org/10.1155/2021/6781541.

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In this paper, we investigate the existence of positive solutions of a class of fractional three-point boundary value problem with an advanced argument by using fixed-point index theory. Our results improve and extend some known results in the literature. Two examples are given to demonstrate the effectiveness of our results.

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12

Muglia, Luigi, and Paolamaria Pietramala. "Second-Order Impulsive Differential Equations with Functional Initial Conditions on Unbounded Intervals." Journal of Function Spaces and Applications 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/479049.

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We present some results on the existence of solutions for second-order impulsive differential equations with deviating argument subject to functional initial conditions. Our results are based on Schaefer's fixed point theorem for completely continuous operators.

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13

Zhang, Xuemei, and Meiqiang Feng. "Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/393187.

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This paper investigates the expression and properties of Green’s function for a second-order singular boundary value problem with integral boundary conditions and delayed argument-x′′t-atx′t+btxt=ωtft, xαt, t∈0, 1; x′0=0, x1-∫01htxtdt=0, wherea∈0, 1, 0, +∞, b∈C0, 1, 0, +∞and,ωmay be singular att=0or/and att=1. Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. Moreover, the approach to express the integral equation of the above problem is different from earlier approaches. Our results cover a second-order boundary value problem without deviating arguments and are compared with some recent results.

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14

Md Asaduzzamana and Md Zulfikar Ali. "Existence of Positive Solution for a Nonlinear Weighted Bi-Harmonic System of Elliptic Partial Differential Equations via Fixed-Point Argument." GANIT: Journal of Bangladesh Mathematical Society 40, no. 1 (July 14, 2020): 54–70. http://dx.doi.org/10.3329/ganit.v40i1.48195.

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In this paper, we establish an existence criterion of positive solution for a nonlinear weighted bi-harmonic system of elliptic partial differential equations in the unit ball in Nn ( dimensionaleuclideanspace) The analysis of this paper is based on a topological method (a fixed-point argument). Initially, we establish a priori solution estimates, and then use a fixed-point theorem for deducing the existence of positive solutions. Finally, we prove a non-existence criterion as the complement of existence criterion. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 54-70

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15

Feng, Jianfeng, and David Brown. "Fixed-Point Attractor Analysis for a Class of Neurodynamics." Neural Computation 10, no. 1 (January 1, 1998): 189–213. http://dx.doi.org/10.1162/089976698300017944.

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Nearly all models in neural networks start from the assumption that the input-output characteristic is a sigmoidal function. On parameter space, we present a systematic and feasible method for analyzing the whole spectrum of attractors—all-saturated, all-but-one-saturated, all-but-twosaturated, and so on—of a neurodynamical system with a saturated sigmoidal function as its input-output characteristic. We present an argument that claims, under a mild condition, that only all-saturated or all but-one-saturated attractors are observable for the neurodynamics. For any given all-saturated configuration [Formula: see text] (all-but-one-saturated configuration [Formula: see text]) the article shows how to construct an exact parameter region R([Formula: see text])([Formula: see text]([Formula: see text])) such that if and only if the parameters fall within R([Formula: see text])([Formula: see text]([Formula: see text])), then [Formula: see text]([Formula: see text]) is an attractor (a fixed point) of the dynamics. The parameter region for an all-saturated fixed-point attractor is independent of the specific choice of a saturated sigmoidal function, whereas for an all-but-one-saturated fixed point, it is sensitive to the input-output characteristic. Based on a similar idea, the role of weight normalization realized by a saturated sigmoidal function in competitive learning is discussed. A necessary and sufficient condition is provided to distinguish two kinds of competitive learning: stable competitive learning with the weight vectors representing extremes of input space and being fixed-point attractors, and unstable competitive learning. We apply our results to Linsker's model and (using extreme value theory in statistics) the Hopfield model and obtain some novel results on these two models.

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16

WU, CHUFEN, and PEIXUAN WENG. "STABILITY OF STEADY STATES AND EXISTENCE OF TRAVELING WAVES FOR A HOST-VECTOR EPIDEMIC." International Journal of Bifurcation and Chaos 21, no. 06 (June 2011): 1667–87. http://dx.doi.org/10.1142/s0218127411029355.

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We study the stability of steady states and establish the existence of traveling waves for a diffusive host-vector epidemic with a nonlocal spatiotemporal interaction. We develop the techniques of contracting-convex-sets, limit argument, singular perturbation and fixed point theorems.

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17

Scarpa, Luca, and Ulisse Stefanelli. "An order approach to SPDEs with antimonotone terms." Stochastics and Partial Differential Equations: Analysis and Computations 8, no. 4 (January 3, 2020): 819–32. http://dx.doi.org/10.1007/s40072-019-00161-7.

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AbstractWe consider a class of parabolic stochastic partial differential equations featuring an antimonotone nonlinearity. The existence of unique maximal and minimal variational solutions is proved via a fixed-point argument for nondecreasing mappings in ordered spaces. This relies on the validity of a comparison principle.

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18

Watkins, Will. "Modified Wiener equations." International Journal of Mathematics and Mathematical Sciences 27, no. 6 (2001): 347–56. http://dx.doi.org/10.1155/s0161171201006561.

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This paper is concerned with a class of functional differential equations whose argument transforms are involutions. In contrast to the earlier works in this area, which have used only involutions with a fixed point, we also admit involutions without a fixed point. In the first case, an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. In our case, either two initial conditions or two boundary conditions are necessary for a solution; the equation is then reduced to a boundary value problem for a higher order ODE.

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19

LI, YONGKUN, and ERLIANG XU. "THREE POSITIVE PERIODIC SOLUTIONS FOR DYNAMIC EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT AND IMPULSE ON TIME SCALES." Glasgow Mathematical Journal 53, no. 2 (December 8, 2010): 369–77. http://dx.doi.org/10.1017/s0017089510000790.

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AbstractIn this paper, by using the Leggett–Williams fixed point theorem, the existence of three positive periodic solutions for differential equations with piecewise constant argument and impulse on time scales is investigated. Some easily verifiable sufficient criteria are established. Finally, an example is given to illustrate the results.

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20

Zhu, Shanliang, Shufang Zhang, Xinli Zhang, and Qingling Li. "Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument." Advances in Mathematical Physics 2020 (March 21, 2020): 1–9. http://dx.doi.org/10.1155/2020/6738247.

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In this paper, the existence and uniqueness of response solutions, which has the same frequency ω with the nonlinear terms, are investigated for a quasiperiodic singularly perturbed system involving reflection of the argument. Firstly, we prove that all quasiperiodic functions with the frequency ω form a Banach space. Then, we obtain the existence and uniqueness of quasiperiodic solutions by means of the fixed-point methods and the B-property of quasiperiodic functions.

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21

Curien, Nicolas, and Adrien Joseph. "Partial match queries in two-dimensional quadtrees: a probabilistic approach." Advances in Applied Probability 43, no. 01 (March 2011): 178–94. http://dx.doi.org/10.1017/s0001867800004742.

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We analyze the mean cost of the partial match queries in random two-dimensional quadtrees. The method is based on fragmentation theory. The convergence is guaranteed by a coupling argument of Markov chains, whereas the value of the limit is computed as the fixed point of an integral equation.

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22

Curien, Nicolas, and Adrien Joseph. "Partial match queries in two-dimensional quadtrees: a probabilistic approach." Advances in Applied Probability 43, no. 1 (March 2011): 178–94. http://dx.doi.org/10.1239/aap/1300198518.

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We analyze the mean cost of the partial match queries in random two-dimensional quadtrees. The method is based on fragmentation theory. The convergence is guaranteed by a coupling argument of Markov chains, whereas the value of the limit is computed as the fixed point of an integral equation.

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23

Nakamura, Takuya. "Sur les arguments sémantiques du verbe expliquer et leur réalisation syntaxique." Actes du «27e colloque international sur le lexique et la grammaire» (L'Aquila, 10-13 septembre 2008). Première partie 32, no. 2 (December 15, 2009): 187–99. http://dx.doi.org/10.1075/li.32.2.03nak.

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In this preliminary descriptive research, taking one French verb (expliquer), we explore syntactic possibilities of argument realization. For this verb, at least four types of syntactic constructions are specified for a fixed set of semantic arguments. When the direct object is realized as a NP (and not as a bare Que P) assuming the role of “object” of explanation, it is observed that the subject can vary between the “agent” and “explanation” roles, in correlation with the change of the origin of “explanation”. This type of difference is to be considered a change of diathesis of the same verb. An agentive construction with a complement clause object happens to be a marginal one from the point of view of argument realization, functioning accidentally as a variant of a sentence with verbs of saying. This type of complement clause is a bare Que P in the sense that it does not manifest an alternation with a Que P headed by le fait.

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24

Neog, Murchana, Mohammed M. M. Jaradat, and Pradip Debnath. "Common Fixed Point Results of Set Valued Maps for Aφ-Contraction and Generalized ϕ-Type Weak Contraction." Symmetry 11, no. 7 (July 8, 2019): 894. http://dx.doi.org/10.3390/sym11070894.

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The solutions for many real life problems may be obtained by interpreting the given problem mathematically in the form f ( x ) = x . One such example is that of the famous Borsuk–Ulam theorem in which, using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this article, some new results concerning coincidence and a common fixed point for an A φ -contraction and a generalized ϕ -type weak contraction are established. We prove our results for set valued maps without using continuity of the corresponding maps and completeness of the relevant space. Our results generalize and extend several existing results. Some new examples are given to demonstrate the generality and non-triviality of our results.

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25

Karthikeyan, Shanmugasundaram, and Krishnan Balachandran. "Constrained controllability of nonlinear stochastic impulsive systems." International Journal of Applied Mathematics and Computer Science 21, no. 2 (June 1, 2011): 307–16. http://dx.doi.org/10.2478/v10006-011-0023-0.

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Constrained controllability of nonlinear stochastic impulsive systemsThis paper is concerned with complete controllability of a class of nonlinear stochastic systems involving impulsive effects in a finite time interval by means of controls whose initial and final values can be assigned in advance. The result is achieved by using a fixed-point argument.

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26

Raheem, A., and M. Kumar. "On controllability for a nondensely defined fractional differential equation with a deviated argument." Mathematical Sciences 13, no. 4 (October 26, 2019): 407–13. http://dx.doi.org/10.1007/s40096-019-00309-5.

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Abstract This article deals with a fractional differential equation with a deviated argument defined on a nondense set. A fixed-point theorem and the concept of measure of noncompactness are used to prove the existence of a mild solution. Furthermore, by using the compactness of associated cosine family, we proved that system is approximately controllable and obtains an optimal control which minimizes the performance index. To illustrate the abstract result, we included an example.

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27

Chiu, Kuo-Shou. "Existence and Global Exponential Stability of Equilibrium for Impulsive Cellular Neural Network Models with Piecewise Alternately Advanced and Retarded Argument." Abstract and Applied Analysis 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/196139.

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We introduce impulsive cellular neural network models with piecewise alternately advanced and retarded argument (in short IDEPCA). The model with the advanced argument is system with strong anticipation. Some sufficient conditions are established for the existence and global exponential stability of a unique equilibrium. The approaches are based on employing Banach’s fixed point theorem and a new IDEPCA integral inequality of Gronwall type. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses and piecewise constant argument deviations, which provides exibility for the design and analysis of cellular neural network models. Several numerical examples and simulations are also given to show the feasibility and effectiveness of our results.

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Dobriţoiu, Maria. "The Existence and Uniqueness of the Solution of a Nonlinear Fredholm–Volterra Integral Equation with Modified Argument via Geraghty Contractions." Mathematics 9, no. 1 (December 24, 2020): 29. http://dx.doi.org/10.3390/math9010029.

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Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and uniqueness conditions for the solution of a nonlinear Fredholm–Volterra integral equation with a modified argument.

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CLAPP, MÓNICA, and TOBIAS WETH. "TWO SOLUTIONS OF THE BAHRI–CORON PROBLEM IN PUNCTURED DOMAINS VIA THE FIXED POINT TRANSFER." Communications in Contemporary Mathematics 10, no. 01 (February 2008): 81–101. http://dx.doi.org/10.1142/s0219199708002715.

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We consider the problem [Formula: see text] where Ω is a bounded smooth domain in ℝN, N ≥ 3, and [Formula: see text] is the critical Sobolev exponent. We assume that Ω is annular shaped, i.e. there are constants R2 > R1 > 0 such that {x ∈ ℝN : R1 < |x| < R2} ⊂ Ω and {x ∈ ℝN : |x| < R1}\Ω ≠ ∅. Coron [7] showed that there is one positive solution to this problem if R2/R1 is large enough. We establish the existence of at least two pairs of nontrivial solutions in this case. The proof combines a deformation argument on the Nehari manifold with cohomological information derived from Dold's fixed point transfer. To deal with the lack of compactness, an energy estimate recently proved by one of the authors is used.

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BEN-EL-MECHAIEKH, HICHEM, and ROBERT W. DIMAND. "VON NEUMANN, VILLE, AND THE MINIMAX THEOREM." International Game Theory Review 12, no. 02 (June 2010): 115–37. http://dx.doi.org/10.1142/s0219198910002556.

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Von Neumann proved the minimax theorem (existence of a saddle-point solution to 2 person, zero sum games) in 1928. While his second article on the minimax theorem, stating the proof, has long been translated from German, his first announcement of his result (communicated in French to the Academy of Sciences in Paris by Borel, who had posed the problem settled by Von Neumann's proof) is translated here for the first time. The proof presented by Von Neumann and Morgenstern (1944) is not Von Neumann's rather involved proof of 1928, but is based on what they called "The Theorem of the Alternative for Matrices" which is in essence a reformulation of an elegant and elementary result by Borel's student Jean Ville in 1938. Ville's argument was the first to bring to light the simplifying role of convexity and to highlight the connection between the existence of minimax and the solvability of systems of linear inequalities. It by-passes nontrivial topological fixed point arguments and allows the treatment of minimax by simpler geometric methods. This approach has inspired a number of seminal contributions in convex analysis including fixed point and coincidence theory for set-valued mappings. Ville's contributions are discussed briefly and von Neuman's original communication, Ville's note, and Borel's commentary on it are translated here for the first time.

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31

DHAGE, BAPURAO C., JANHAVI B. DHAGE, and JAVID ALI. ""Monotone iteration method for general nonlinear two point boundary value problems with deviating arguments"." Carpathian Journal of Mathematics 38, no. 2 (February 28, 2022): 405–15. http://dx.doi.org/10.37193/cjm.2022.02.11.

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"In this paper we shall study the existence and approximation results for a nonlinear two point boundary value problem of a second order ordinary differential equation with general form of Dirichlet/Neumann type boundary conditions. The nonlinearity present on right hand side of the differential equation is assumed to be Caratho´eodory containing a deviating argument. The proofs of the main results are based on a monotone iteration method contained in the hybrid fixed point principles of Dhage (2014) in an ordered Banach space. Finally, some remarks concerning the merits of our monotone iteration method over other frequently used iteration methods in the theory of nonlinear differential equations are given in the conclusion."

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32

Chiu, Kuo-Shou. "Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument." Scientific World Journal 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/514854.

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We investigate the existence of the periodic solutions of a nonlinear integro-differential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such equations are obtained. In the process we use Green’s function for periodic solutions and convert the given DEPCAG into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. Appropriate examples are given to show the feasibility of our results.

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BENKHALTI, RACHID, ABDELHAI ELAZZOUZI, and KHALIL EZZINBI. "PERIODIC SOLUTIONS FOR SOME NONLINEAR PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS." International Journal of Bifurcation and Chaos 20, no. 02 (February 2010): 545–55. http://dx.doi.org/10.1142/s0218127410025600.

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In this work, we study the existence of periodic solutions for some nonlinear partial functional differential equation of neutral type. We assume that the linear part is nondensely defined and satisfies the Hille–Yosida condition. The delayed part is assumed to be ω-periodic with respect to the first argument. Using a fixed point theorem for multivalued mapping, some sufficient conditions are given to prove the existence of periodic solutions.

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Munteanu, Ionuţ. "Feedback exponential stabilization of the semilinear heat equation with nonlocal initial conditions." Nonlinear Analysis: Modelling and Control 26, no. 6 (November 1, 2021): 1106–22. http://dx.doi.org/10.15388/namc.2021.26.24809.

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The present paper is devoted to the problem of stabilization of the one-dimensional semilinear heat equation with nonlocal initial conditions. The control is with boundary actuation. It is linear, of finite-dimensional structure, given in an explicit form. It allows to write the corresponding solution of the closed-loop equation in a mild formulation via a kernel, then to apply a fixed point argument in a convenient space.

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35

Blömker, Dirk, Giuseppe Cannizzaro, and Marco Romito. "Random initial conditions for semi-linear PDEs." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 3 (January 29, 2019): 1533–65. http://dx.doi.org/10.1017/prm.2018.157.

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AbstractWe analyse the effect of random initial conditions on the local well-posedness of semi-linear PDEs, to investigate to what extent recent ideas on singular stochastic PDEs can prove useful in this framework.In particular, in some cases, stochastic initial conditions extend the validity of the fixed-point argument to larger spaces than deterministic initial conditions would allow, but in general, it is never possible to go beyond the threshold that is predicted by critical scaling, as in our general class of equations we are not exploiting any special structure present in the equation.We also give a specific example where the level of regularity for the fixed-point argument reached by random initial conditions is not yet critical, but it is already sharp in the sense that we find infinitely many random initial conditions of slightly lower regularity, where there is no solution at all. Thus criticality cannot be reached even by random initial conditions.The existence and uniqueness in a critical space is always delicate, but we can consider the Burgers equation in logarithmically sub-critical spaces, where existence and uniqueness hold, and again random initial conditions allow to extend the validity to spaces of lower regularity which are still logarithmically sub-critical.

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36

Li, Haiyan, and Jianguo Gao. "Qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source." International Journal of Biomathematics 09, no. 04 (April 22, 2016): 1650051. http://dx.doi.org/10.1142/s1793524516500510.

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In this paper, we focus on the qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source. Applying a fixed point argument, [Formula: see text]-estimate technique and Moser’s iteration, we derive that the model admits a unique global solution provided the initial cell mass satisfying [Formula: see text] for [Formula: see text] While for [Formula: see text], there are no restrictions on the initial cell mass and the result still holds.

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FANG, YUNG-FU. "LOCAL EXISTENCE FOR SEMILINEAR WAVE EQUATIONS AND APPLICATIONS TO YANG–MILLS EQUATIONS." Journal of Hyperbolic Differential Equations 02, no. 01 (March 2005): 61–76. http://dx.doi.org/10.1142/s0219891605000373.

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In this work we are concerned with a local existence of certain semi-linear wave equations for which the initial data has minimal regularity. Assuming the initial data are in H1+∊ and H∊ for any ∊ > 0, we prove a local result by using a fixed point argument, the main ingredient being an a priori estimate for the quadratic nonlinear term uDu. The technique applies to the Yang–Mills equations in the Lorentz gauge.

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38

Zhao, Kaihong. "Multiple positive solutions of integral boundary value problem for a class of nonlinear fractional-order differential coupling system with eigenvalue argument and (p1,p2)-Laplacian." Filomat 32, no. 12 (2018): 4291–306. http://dx.doi.org/10.2298/fil1812291z.

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This paper is concerned with the integral boundary value problem for a class of nonlinear fractional order differential coupling system with eigenvalue argument and (p1,p2)-Laplacian. Some sufficient criteria have been established to guarantee the existence and multiplicity of positive solution by the fixed point index theorem in cones. Meanwhile, we obtain the range of eigenvalue parameter. As an application, one example is also provided to illustrate the validity of our main results.

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39

Wang, Yi, Wei-dong Song, Dan Fang, and Qing-wei Guo. "Guidance and Control Design for a Class of Spin-Stabilized Projectiles with a Two-Dimensional Trajectory Correction Fuze." International Journal of Aerospace Engineering 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/908304.

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A guidance and control strategy for a class of 2D trajectory correction fuze with fixed canards is developed in this paper. Firstly, correction control mechanism is researched through studying the deviation motion, the key point of which is the dynamic equilibrium angle. Phase lag of swerve response is the dominating factor for correction control, and formula is deduced with the Mach number as argument. Secondly, impact point deviation prediction based on perturbation theory is proposed, and the numerical solution and application method are introduced. Finally, guidance and control strategy is developed, and simulations to validate the strategy are conducted.

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ASHBAUGH, MARK S., and RAFAEL D. BENGURIA. "THE RANGE OF VALUES OF λ2/λ1 AND λ3/λ1 FOR THE FIXED MEMBRANE PROBLEM." Reviews in Mathematical Physics 06, no. 05a (January 1994): 999–1009. http://dx.doi.org/10.1142/s0129055x9400033x.

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We investigate the region of the plane in which the point (λ2/λ1, λ3/λ1) can lie, where λ1, λ2, and λ3 are the first three eigenvalues of the Dirichlet Laplacian on an arbitrary bounded domain Ω ⊂ ℝ2. In particular, by making use of a technique introduced by de Vries we obtain the best bounds to date for the quantities λ3/λ1 and (λ2 + λ3)/λ1. These bounds are λ3/λ1 ≤ 3.90514+ and (λ2 + λ3)/λ1 ≤ 5.52485+ and give small improvements over previous bounds of Marcellini. Where Marcellini used a bound due to Brands in his argument we use a better version of this bound which we obtain by incorporating deVries' idea. The other bounds that yield the greatest information about the region where points (λ2/λ1, λ3/λ1) can (possibly) lie are those due to Marcellini, Hile and Protter, and us (of which there are several, with two of them being new with this paper).

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41

Barlak, Selçuk, and Gábor Szabó. "On diagonal quasi-free automorphisms of simple Cuntz-Krieger algebras." MATHEMATICA SCANDINAVICA 125, no. 2 (October 19, 2019): 210–26. http://dx.doi.org/10.7146/math.scand.a-114823.

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We show that an outer action of a finite abelian group on a simple Cuntz-Krieger algebra is strongly approximately inner in the sense of Izumi if the action is given by diagonal quasi-free automorphisms and the associated matrix is aperiodic. This is achieved by an approximate cohomology vanishing-type argument for the canonical shift restricted to the relative commutant of the set of domain projections of the canonical generating isometries in the fixed point algebra.

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42

Ding, Yonghong, and Yongxiang Li. "Approximate controllability of fractional stochastic evolution equations with nonlocal conditions." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 7-8 (November 18, 2020): 829–41. http://dx.doi.org/10.1515/ijnsns-2019-0229.

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AbstractThis paper deals with the approximate controllability for a class of fractional stochastic evolution equations with nonlocal initial conditions in a Hilbert space. We delete the compactness condition or Lipschitz condition for nonlocal term appearing in various literatures, and only need to suppose some weak growth condition on the nonlocal term. The discussion is based on the fixed point theorem, diagonal argument and approximation techniques. In the end, an example is presented to illustrate the abstract theory.

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Dond, Asha K., and Amiya K. Pani. "A Priori and A Posteriori Estimates of Conforming and Mixed FEM for a Kirchhoff Equation of Elliptic Type." Computational Methods in Applied Mathematics 17, no. 2 (April 1, 2017): 217–36. http://dx.doi.org/10.1515/cmam-2016-0041.

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AbstractIn this article, a priori and a posteriori estimates of conforming and expanded mixed finite element methods for a Kirchhoff equation of elliptic type are derived. For the expanded mixed finite element method, a variant of Brouwer’s fixed point argument combined with a monotonicity argument yields the well-posedness of the discrete nonlinear system. Further, a use of both Helmholtz decomposition of $L^{2}$-vector valued functions and the discrete Helmholtz decomposition of the Raviart–Thomas finite elements helps in a crucial way to achieve optimal a priori as well as a posteriori error bounds. For both conforming and expanded mixed form, reliable and efficient a posteriori estimators are established. Finally, the numerical experiments are performed to validate the theoretical convergence rates.

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Tao, Mengfei, and Binlin Zhang. "Solutions for nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities." Advances in Nonlinear Analysis 11, no. 1 (January 1, 2022): 1332–51. http://dx.doi.org/10.1515/anona-2022-0248.

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Abstract In this article, we aimed to study a class of nonhomogeneous fractional (p, q)-Laplacian systems with critical nonlinearities as well as critical Hardy nonlinearities in R N {{\mathbb{R}}}^{N} . By appealing to a fixed point result and fractional Hardy-Sobolev inequality, the existence of nontrivial nonnegative solutions is obtained. In particular, we also consider Choquard-type nonlinearities in the second part of this article. More precisely, with the help of Hardy-Littlewood-Sobolev inequality, we obtain the existence of nontrivial solutions for the related systems based on the same approach. Finally, we obtain the corresponding existence results for the fractional (p, q)-Laplacian systems in the case of N = s p = l q N=sp=lq . It is worth pointing out that using fixed point argument to seek solutions for a class of nonhomogeneous fractional (p, q)-Laplacian systems is the main novelty of this article.

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Liu, Zhenhai, and Nikolaos S. Papageorgiou. "Positive Solutions for Resonant (p, q)-equations with convection." Advances in Nonlinear Analysis 10, no. 1 (July 17, 2020): 217–32. http://dx.doi.org/10.1515/anona-2020-0108.

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Abstract We consider a nonlinear parametric Dirichlet problem driven by the (p, q)-Laplacian (double phase problem) with a reaction exhibiting the competing effects of three different terms. A parametric one consisting of the sum of a singular term and of a drift term (convection) and of a nonparametric perturbation which is resonant. Using the frozen variable method and eventually a fixed point argument based on an iterative asymptotic process, we show that the problem has a positive smooth solution.

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Arada, N., and A. Sequeira. "Strong Steady Solutions for a Generalized Oldroyd-B Model with Shear-Dependent Viscosity in a Bounded Domain." Mathematical Models and Methods in Applied Sciences 13, no. 09 (September 2003): 1303–23. http://dx.doi.org/10.1142/s0218202503002921.

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We study a system of nonlinear partial differential equations governing the motion of an incompressible viscoelastic fluid of Oldroyd type in a bounded domain, with a non-Newtonian viscosity depending on the second invariant of the rate of deformation tensor. Considering the equations in a suitably decomposed form, we establish, for small and suitably regular data, existence of a unique solution using a fixed point argument in an appropriate functional setting. This model includes the classical Oldroyd-B fluid as a particular case.

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LI, XIAOLI, NING SU, and DEHUA WANG. "LOCAL STRONG SOLUTION TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC FLOW WITH LARGE DATA." Journal of Hyperbolic Differential Equations 08, no. 03 (September 2011): 415–36. http://dx.doi.org/10.1142/s0219891611002457.

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The three-dimensional compressible magnetohydrodynamic isentropic flow with zero magnetic diffusivity is studied in this paper. The vanishing magnetic diffusivity causes significant difficulties due to the loss of dissipation of the magnetic field. The existence and uniqueness of local-in-time strong solutions with large initial data is established. Strong solutions have weaker regularity than classical solutions. A generalized Lax–Milgram theorem and a Schauder–Tychonoff-type fixed-point argument are applied on conjunction with novel techniques and estimates for strong solutions.

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Lin, Yiqing, and Abdoulaye Soumana Hima. "Reflected stochastic differential equations driven by G-Brownian motion in non-convex domains." Stochastics and Dynamics 19, no. 03 (May 30, 2019): 1950025. http://dx.doi.org/10.1142/s0219493719500254.

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In this paper, we first review the penalization method for solving deterministic Skorokhod problems in non-convex domains and establish estimates for problems with [Formula: see text]-Hölder continuous functions. With the help of these results obtained previously for deterministic problems, we pathwisely define the reflected [Formula: see text]-Brownian motion and prove its existence and uniqueness in a Banach space. Finally, multi-dimensional reflected stochastic differential equations driven by [Formula: see text]-Brownian motion are investigated via a fixed-point argument.

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Farwig, Reinhard, and Andreas Schmidt. "Weak Solutions to a Fluid-Structure Interaction Model of a Viscous Fluid with an Elastic Plate under Coulomb Friction Coupling." Mathematics 9, no. 9 (May 1, 2021): 1026. http://dx.doi.org/10.3390/math9091026.

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We consider the behavior of a viscous fluid within a container that has an elastic upper, free boundary. The movement of the upper boundary is described by a combination of a plate equation and a boundary condition of friction type that quantifies the elasticity of the boundary. We show the local existence of weak solutions to this coupled system in three dimensions, by applying the Galerkin method to a regularized version of the problem and using a fixed-point argument afterwards.

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50

Wei, Shihshu Walter, and Ye Li. "Generalized sharp Hardy type and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds." Tamkang Journal of Mathematics 40, no. 4 (December 23, 2009): 401–13. http://dx.doi.org/10.5556/j.tkjm.40.2009.604.

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We prove generalized Hardy's type inequalities with sharp constants and Caffarelli-Kohn-Nirenberg inequalities with sharp constants on Riemannian manifolds $M$. When the manifold is Euclidean space we recapture the sharp Caffarelli-Kohn-Nirenberg inequality. By using a double limiting argument, we obtain an inequality that implies a sharp Hardy's inequality, for functions with compact support on the manifold $M $ (that is, not necessarily on a punctured manifold $ M \backslash \{ x_0 \} $ where $x_0$ is a fixed point in $M$). Some topological and geometric applications are discussed.

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