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Relevant bibliographies by topics / Multiple T-periodic solutions

Academic literature on the topic 'Multiple T-periodic solutions'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Multiple T-periodic solutions"

1

Kyritsi, Sophia Th, and Nikolaos S. Papageorgiou. "Multiple Solutions for Nonlinear Periodic Problems." Canadian Mathematical Bulletin 56, no. 2 (June 1, 2013): 366–77. http://dx.doi.org/10.4153/cmb-2011-154-5.

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Abstract We consider a nonlinear periodic problem driven by a nonlinear nonhomogeneous differential operator and a Carathéodory reaction term f (t; x) that exhibits a (p – 1)-superlinear growth in x 2 R near 1 and near zero. A special case of the differential operator is the scalar p-Laplacian. Using a combination of variational methods based on the critical point theory with Morse theory (critical groups), we show that the problem has three nontrivial solutions, two of which have constant sign (one positive, the other negative).

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2

Liu, Youjun, Huanhuan Zhao, and Jurang Yan. "Existence of Positive Periodic Solutions forn-Dimensional Nonautonomous System." Discrete Dynamics in Nature and Society 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/268418.

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In this paper we consider the existence, multiplicity, and nonexistence of positive periodic solutions forn-dimensional nonautonomous functional differential systemx'(t)=H(t,x(t))-λB(t)F(x(t-τ(t))), wherehiareω-periodic intand there existω-periodic functionsαi,βi∈C(R,R+)such thatαi(t)≤(hi(t,x)/xi)≤βi(t),∫0ω‍αi(t)dt>0,forx∈R+nall withxi>0,andt∈R,limxi→0+(hi(t,x)/xi)exist fort∈R;bi∈C(R,R+)areω-periodic functions and∫0ω‍bi(t)dt>0;fi∈C(R+n,R+),fi(x)>0forx >0;τ∈(R,R)is anω-periodic function. We show that the system has multiple or no positiveω-periodic solutions for sufficiently large or smallλ>0, respectively.

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3

Li, Qiang, and Yongxiang Li. "On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays." Abstract and Applied Analysis 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/929870.

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The existence results of positiveω-periodic solutions are obtained for the second-order functional differential equation with multiple delaysu″(t)+a(t)u(t)=f(t,u(t),u(t−τ1(t)),…,u(t−τn(t))), wherea(t)∈C(ℝ)is a positiveω-periodic function,f:ℝ×[0,+∞)n+1→[0,+∞)is a continuous function which isω-periodic int, andτ1(t),…,τn(t)∈C(ℝ,[0,+∞))areω-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary problem. Our discussion is based on the fixed-point index theory in cones.

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4

Wang, Zhenguo, and Qiuying Li. "Multiple periodic solutions for discrete boundary value problem involving the mean curvature operator." Open Mathematics 20, no. 1 (January 1, 2022): 1195–202. http://dx.doi.org/10.1515/math-2022-0509.

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Abstract In this article, by using critical point theory, we prove the existence of multiple T T -periodic solutions for difference equations with the mean curvature operator: − Δ ( ϕ c ( Δ u ( t − 1 ) ) ) + q ( t ) u ( t ) = λ f ( t , u ( t ) ) , t ∈ Z , -\Delta ({\phi }_{c}\left(\Delta u\left(t-1)))+q\left(t)u\left(t)=\lambda f\left(t,u\left(t)),\hspace{1em}t\in {\mathbb{Z}}, where Z {\mathbb{Z}} is the set of integers. As a T T -periodic problem, it does not require the nonlinear term is unbounded or bounded, and thus, our results are supplements to some well-known periodic problems. Finally, we give one example to illustrate our main results.

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5

OBERSNEL, FRANCO, and PIERPAOLO OMARI. "MULTIPLE BOUNDED VARIATION SOLUTIONS OF A PERIODICALLY PERTURBED SINE-CURVATURE EQUATION." Communications in Contemporary Mathematics 13, no. 05 (October 2011): 863–83. http://dx.doi.org/10.1142/s0219199711004488.

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We prove the existence of at least two T-periodic solutions, not differing from each other by an integer multiple of 2π, of the sine-curvature equation [Formula: see text] We assume that A ∈ ℝ and [Formula: see text] is a T-periodic function such that [Formula: see text] and, e.g. ‖h‖L∞ < 4/T. Our approach is variational and makes use of basic results of non-smooth critical point theory in the space of bounded variation functions.

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6

Zhang, Hong, and Junxia Meng. "Periodic Solutions for Duffing Typep-Laplacian Equation with Multiple Constant Delays." Abstract and Applied Analysis 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/760918.

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Using inequality techniques and coincidence degree theory, new results are provided concerning the existence and uniqueness of periodic solutions for the Duffing typep-Laplacian equation with multiple constant delays of the form(φp(x′(t)))′+Cx′(t)+g0(t,x(t))+∑k=1ngk(t,x(t-τk))=e(t).Moreover, an example is provided to illustrate the effectiveness of the results in this paper.

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7

Luo, Zhenguo. "Multiple Positive Periodic Solutions for Two Kinds of Higher-Dimension Impulsive Differential Equations with Multiple Delays and Two Parameters." Journal of Mathematics 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/214093.

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By applying the fixed point theorem, we derive some new criteria for the existence of multiple positive periodic solutions for two kinds of n-dimension periodic impulsive functional differential equations with multiple delays and two parameters:xi′(t)=ai(t)xi(t)-λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn(t)))), a.e.,t>0,t≠tk,k∈Z+,xi(tk+)-xi(tk-)=μcikxi(tk),i=1,2,…,n,k∈Z+,andxi′(t)=-ai(t)xi(t)+λbi(t)fi(t,x(t),x(t-τ1(t)),…,x(t-τn(t)))), a.e.,t>0,t≠tk,k∈Z+,xi(tk+)-xi(tk-)=μcikxi(tk),i=1,2,…,n,k∈Z+.As an application, we study some special cases of the previous systems, which have been studied extensively in the literature.

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8

Pinto, Manuel, and Sergei Trofimchuk. "Stability and existence of multiple periodic solutions for a quasilinear differential equation with maxima." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 5 (October 2000): 1103–18. http://dx.doi.org/10.1017/s0308210500000597.

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We study the stability of periodic solutions of the scalar delay differential equation where f(t) is a periodic forcing term and δ,p∈R. We study stability in the first approximation showing that the non-smooth equation (*) can be linearized along some ‘non-singular’ periodic solutions. Then the corresponding variational equation together with the Krasnosel'skij index are used to prove the existence of multiple periodic solutions to (*). Finally, we apply a generalization of Halanay's inequality to establish conditions for global attractivity in equations with maxima.

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9

Lu, Shiping, and Ming Lu. "Periodic Solutions for a Prescribed Mean Curvature Equation with Multiple Delays." Journal of Applied Mathematics 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/909252.

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We study the existence of periodic solutions for the one-dimensional prescribed mean curvature delay equation(d/dt)(x'(t)/1+x't2) +∑i=1naitgxt-τit=pt. By using Mawhin's continuation theorem, a new result is obtained. Furthermore, the nonexistence of periodic solution for the equation is investigated as well.

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10

Ji, Shuguan, and Yong Li. "Time-periodic solutions to the one-dimensional wave equation with periodic or anti-periodic boundary conditions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 137, no. 2 (2007): 349–71. http://dx.doi.org/10.1017/s0308210505001174.

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This paper is devoted to the study of time-periodic solutions to the nonlinear one-dimensional wave equation with x-dependent coefficients u(x)ytt – (u(x)yx)x + g(x,t,y) = f(x,t) on (0,π) × ℝ under the periodic boundary conditions y(0,t) = y(π,t), yx(0,t) = yx(π,t) or anti-periodic boundary conditions y(0, t) = –y(π,t), yx[0,t) = – yx(π,t). Such a model arises from the forced vibrations of a non-homogeneous string and the propagation of seismic waves in non-isotropic media. Our main concept is that of the ‘weak solution’. For T, the rational multiple of π, we prove some important properties of the weak solution operator. Based on these properties, the existence and regularity of weak solutions are obtained.

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