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Journal articles on the topic 'Existence and multiplicity results'

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Published: 10 March 2023

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1

Bereanu, Cristian, and Jean Mawhin. "Existence and multiplicity results for nonlinear second order difference equations with Dirichlet boundary conditions." Mathematica Bohemica 131, no. 2 (2006): 145–60. http://dx.doi.org/10.21136/mb.2006.134087.

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2

Rudolf, Boris. "An existence and multiplicity result for a periodic boundary value problem." Mathematica Bohemica 133, no. 1 (2008): 41–61. http://dx.doi.org/10.21136/mb.2008.133946.

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3

Goeleven, D., V. H. Nguyen, and M. Willem. "Existence and multiplicity results for semicoercive unilateral problems." Bulletin of the Australian Mathematical Society 49, no. 3 (June 1994): 489–97. http://dx.doi.org/10.1017/s0004972700016592.

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In this paper, we investigate a general class of variational inequalities. Existence and multiplicity results are obtained by using minimax principles for lower semicontinuous functions due to A. Szulkin.

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4

Dong, Wei. "Existence and multiplicity results for quasilinear elliptic equations." Bulletin of the Australian Mathematical Society 71, no. 3 (June 2005): 377–86. http://dx.doi.org/10.1017/s0004972700038375.

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The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear elliptic equations. Based on the mountain pass theorems and sub-and supersolutions argument for p-Laplacian operators, under suitable conditions on nonlinearity f(x, s), we show the follwing problem: , where Ω is a bounded open subset of RN, N ≥ 2, with smooth boundary, λ is a positive parameter and ∆p is the p-Laplacian operator with p > 1, possesses at least two positive solutions for large λ.

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5

Huy, Nguyen Bich, Bui The Quan, and Nguyen Huu Khanh. "Existence and multiplicity results for generalized logistic equations." Nonlinear Analysis 144 (October 2016): 77–92. http://dx.doi.org/10.1016/j.na.2016.06.001.

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6

Liu, Wulong, and Guowei Dai. "Existence and multiplicity results for double phase problem." Journal of Differential Equations 265, no. 9 (November 2018): 4311–34. http://dx.doi.org/10.1016/j.jde.2018.06.006.

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7

Baraket, Sami, and Giovanni Molica Bisci. "Multiplicity results for elliptic Kirchhoff-type problems." Advances in Nonlinear Analysis 6, no. 1 (February 1, 2017): 85–93. http://dx.doi.org/10.1515/anona-2015-0168.

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AbstractThe aim of this paper is to establish the existence of multiple solutions for a perturbed Kirchhoff-type problem depending on two real parameters. More precisely, we show that an appropriate oscillating behaviour of the nonlinear part, even under small perturbations, ensures the existence of at least three nontrivial weak solutions. Our approach combines variational methods with properties of nonlocal fractional operators.

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8

Filippakis, Michael, Leszek Gasiński, and Nikolaos S. Papageorgiou. "Multiplicity Results for Nonlinear Neumann Problems." Canadian Journal of Mathematics 58, no. 1 (February 1, 2006): 64–92. http://dx.doi.org/10.4153/cjm-2006-004-6.

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AbstractIn this paper we study nonlinear elliptic problems of Neumann type driven by the p-Laplacian differential operator. We look for situations guaranteeing the existence of multiple solutions. First we study problems which are strongly resonant at infinity at the first (zero) eigenvalue. We prove five multiplicity results, four for problems with nonsmooth potential and one for problems with a C1-potential. In the last part, for nonsmooth problems in which the potential eventually exhibits a strict super-p-growth under a symmetry condition, we prove the existence of infinitely many pairs of nontrivial solutions. Our approach is variational based on the critical point theory for nonsmooth functionals. Also we present some results concerning the first two elements of the spectrum of the negative p-Laplacian with Neumann boundary condition.

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9

Dong, Xiaojing, and Anmin Mao. "Existence and Multiplicity Results for General Quasilinear Elliptic Equations." SIAM Journal on Mathematical Analysis 53, no. 4 (January 2021): 4965–84. http://dx.doi.org/10.1137/20m1350741.

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10

Arioli, Gianni, and Filippo Gazzola. "Existence and multiplicity results for quasilinear elliptic differential systems." Communications in Partial Differential Equations 25, no. 1-2 (January 2000): 125–53. http://dx.doi.org/10.1080/03605300008821510.

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11

He, Wei, Dongdong Qin, and Qingfang Wu. "Existence, multiplicity and nonexistence results for Kirchhoff type equations." Advances in Nonlinear Analysis 10, no. 1 (October 30, 2020): 616–35. http://dx.doi.org/10.1515/anona-2020-0154.

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Abstract In this paper, we study following Kirchhoff type equation: $$\begin{array}{} \left\{ \begin{array}{lll} -\left(a+b\int_{{\it\Omega}}|\nabla u|^2 \mathrm{d}x \right){\it\Delta} u=f(u)+h~~&\mbox{in}~~{\it\Omega}, \\ u=0~~&\mbox{on}~~ \partial{\it\Omega}. \end{array} \right. \end{array}$$ We consider first the case that Ω ⊂ ℝ3 is a bounded domain. Existence of at least one or two positive solutions for above equation is obtained by using the monotonicity trick. Nonexistence criterion is also established by virtue of the corresponding Pohožaev identity. In particular, we show nonexistence properties for the 3-sublinear case as well as the critical case. Under general assumption on the nonlinearity, existence result is also established for the whole space case that Ω = ℝ3 by using property of the Pohožaev identity and some delicate analysis.

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12

Grossi, M. "Existence and multiplicity results for the nonlinear Schrödinger equations." Nonlinear Analysis: Theory, Methods & Applications 47, no. 9 (August 2001): 6009–17. http://dx.doi.org/10.1016/s0362-546x(01)00693-9.

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13

Benalili, Mohammed, and Kamel Tahri. "Nonlinear elliptic fourth order equations existence and multiplicity results." Nonlinear Differential Equations and Applications NoDEA 18, no. 5 (March 5, 2011): 539–56. http://dx.doi.org/10.1007/s00030-011-0106-5.

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14

Kim, Chan-Gyun, and Yong-Hoon Lee. "Existence and multiplicity results for nonlinear boundary value problems." Computers & Mathematics with Applications 55, no. 12 (June 2008): 2870–86. http://dx.doi.org/10.1016/j.camwa.2007.09.007.

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15

Afrouzi, Ghasem, M. Mirzapour, and Vicenţiu Rădulescu. "Existence and multiplicity results for anisotropic stationary Schrödinger equations." Rendiconti Lincei - Matematica e Applicazioni 25, no. 1 (2014): 91–108. http://dx.doi.org/10.4171/rlm/669.

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16

Castro, Alfonso, Jorge Cossio, Sigifredo Herrón, and Carlos Vélez. "Existence and multiplicity results for a semilinear elliptic problem." Journal of Mathematical Analysis and Applications 475, no. 2 (July 2019): 1493–501. http://dx.doi.org/10.1016/j.jmaa.2019.03.028.

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17

Wei, Yucheng, Shaoyun Shi, and Guanggang Liu. "Existence and multiplicity results for partially superquadratic elliptic systems." Applied Mathematics Letters 26, no. 2 (February 2013): 290–95. http://dx.doi.org/10.1016/j.aml.2012.09.010.

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18

Dong, Wei, and Jian Tao Chen. "Existence and Multiplicity Results for a Degenerate Elliptic Equation." Acta Mathematica Sinica, English Series 22, no. 3 (March 14, 2006): 665–70. http://dx.doi.org/10.1007/s10114-005-0696-0.

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19

Dávila, Gonzalo, Alexander Quaas, and Erwin Topp. "Existence, nonexistence and multiplicity results for nonlocal Dirichlet problems." Journal of Differential Equations 266, no. 9 (April 2019): 5971–97. http://dx.doi.org/10.1016/j.jde.2018.10.046.

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20

Chen, Kuan-Ju. "Multiplicity results for some nonlinear elliptic problems." Journal of the Australian Mathematical Society 76, no. 2 (April 2004): 247–68. http://dx.doi.org/10.1017/s1446788700008934.

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AbstractIn this paper, first, we study the existence of the positive solutions of the nonlinear elliptic equations in unbounded domains. The existence is affected by the properties of the geometry and the topology of the domain. We assert that if there exists a (PS)c-sequence with c belonging to a suitable interval depending by the equation, then a ground state solution and a positive higher energy solution exist, too. Next, we study the upper half strip with a hole. In this case, the ground state solution does not exist, however there exists at least a positive higher energy solution.

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21

Papageorgiou, Nikolaos, and Francesca Papalini. "Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities." Annales Polonici Mathematici 75, no. 2 (2000): 125–41. http://dx.doi.org/10.4064/ap-75-2-125-141.

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22

Tang, Yue, Chun-Lei Tang, and Xing-Ping Wu. "Existence and multiplicity results for semilinear elliptic equations at resonance." Bulletin of the Belgian Mathematical Society - Simon Stevin 21, no. 2 (May 2014): 365–78. http://dx.doi.org/10.36045/bbms/1400592631.

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23

Iannizzotto, Antonio, and Nikolaos S. Papageorgiou. "Existence and multiplicity results for resonant fractional boundary value problems." Discrete & Continuous Dynamical Systems - S 11, no. 3 (2018): 511–32. http://dx.doi.org/10.3934/dcdss.2018028.

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24

Moschetto, Danila Sandra. "Existence and multiplicity results for a nonlinear stationary Schrödinger equation." Annales Polonici Mathematici 99, no. 1 (2010): 39–43. http://dx.doi.org/10.4064/ap99-1-3.

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25

Papalini, Francesca. "Nonlinear Periodic Systems with thep-Laplacian: Existence and Multiplicity Results." Abstract and Applied Analysis 2007 (2007): 1–23. http://dx.doi.org/10.1155/2007/80394.

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We study second-order nonlinear periodic systems driven by the vectorp-Laplacian with a nonsmooth, locally Lipschitz potential function. Under minimal and natural hypotheses on the potential and using variational methods based on the nonsmooth critical point theory, we prove existence theorems and a multiplicity result. We conclude the paper with an existence theorem for the scalar problem, in which the energy functional is indefinite (unbounded from both above and below).

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26

Musina, Roberta. "Planar loops with prescribed curvature: Existence, multiplicity and uniqueness results." Proceedings of the American Mathematical Society 139, no. 12 (December 1, 2011): 4445–59. http://dx.doi.org/10.1090/s0002-9939-2011-10915-8.

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27

Drábek, Pavel. "Asymptotic bifurcation problems for quasilinear equations existence and multiplicity results." Topological Methods in Nonlinear Analysis 25, no. 1 (March 1, 2005): 183. http://dx.doi.org/10.12775/tmna.2005.009.

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28

Amster, P., J. P. Borgna, M. C. Mariani, and D. F. Rial. "Existence and Multiplicity Results for the Nonlinear Klein-Gordon Equation." Applicable Analysis 82, no. 9 (September 2003): 895–903. http://dx.doi.org/10.1080/0003681031000154936.

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29

Yang, Ming-Hai, and Zhi-Qing Han. "Existence and multiplicity results for the nonlinear Schrödinger–Poisson systems." Nonlinear Analysis: Real World Applications 13, no. 3 (June 2012): 1093–101. http://dx.doi.org/10.1016/j.nonrwa.2011.07.008.

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30

Boureanu, Maria-Magdalena, and Diana Nicoleta Udrea. "Existence and multiplicity results for elliptic problems with —Growth conditions." Nonlinear Analysis: Real World Applications 14, no. 4 (August 2013): 1829–44. http://dx.doi.org/10.1016/j.nonrwa.2012.12.001.

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31

Faraci, Francesca, Antonio Iannizzotto, Pál Kupán, and Csaba Varga. "Existence and multiplicity results for hemivariational inequalities with two parameters." Nonlinear Analysis: Theory, Methods & Applications 67, no. 9 (November 2007): 2654–69. http://dx.doi.org/10.1016/j.na.2006.09.030.

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32

Filippakis, Michael E. "Existence and multiplicity results for nonlinear nonautonomous second-order systems." Nonlinear Analysis: Theory, Methods & Applications 68, no. 6 (March 2008): 1611–26. http://dx.doi.org/10.1016/j.na.2006.12.046.

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33

Su, Jiabao. "Existence and multiplicity results for classes of elliptic resonant problems." Journal of Mathematical Analysis and Applications 273, no. 2 (September 2002): 565–79. http://dx.doi.org/10.1016/s0022-247x(02)00274-3.

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34

Jiu, Quansen, and Jiabao Su. "Existence and multiplicity results for Dirichlet problems with p-Laplacian." Journal of Mathematical Analysis and Applications 281, no. 2 (May 2003): 587–601. http://dx.doi.org/10.1016/s0022-247x(03)00165-3.

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35

Ou, Zeng-Qi, and Chun-Lei Tang. "Existence and multiplicity results for some elliptic systems at resonance." Nonlinear Analysis: Theory, Methods & Applications 71, no. 7-8 (October 2009): 2660–66. http://dx.doi.org/10.1016/j.na.2009.01.106.

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36

Hao, Xinan, Lishan Liu, and Yonghong Wu. "Existence and multiplicity results for nonlinear periodic boundary value problems." Nonlinear Analysis: Theory, Methods & Applications 72, no. 9-10 (May 2010): 3635–42. http://dx.doi.org/10.1016/j.na.2009.12.044.

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37

Njoku, F. I., and F. Zanolin. "Positive solutions for two-point BVP's: existence and multiplicity results." Nonlinear Analysis: Theory, Methods & Applications 13, no. 11 (January 1989): 1329–38. http://dx.doi.org/10.1016/0362-546x(89)90016-3.

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38

Gasiński, Leszek. "Existence and multiplicity results for quasilinear hemivariational inequalities at resonance." Mathematische Nachrichten 281, no. 12 (December 2008): 1728–46. http://dx.doi.org/10.1002/mana.200510710.

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39

Lü, Dengfeng. "Existence and multiplicity results for critical growth polyharmonic elliptic systems." Mathematical Methods in the Applied Sciences 37, no. 4 (May 28, 2013): 581–96. http://dx.doi.org/10.1002/mma.2816.

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40

Chen, Huiwen, and Zhimin He. "Existence and multiplicity results for the nonlinear Schrödinger-Maxwell systems." Mathematical Methods in the Applied Sciences 38, no. 18 (February 2, 2015): 5005–22. http://dx.doi.org/10.1002/mma.3420.

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41

Bennaoum, A. K., C. Troestler, and M. Willem. "Existence and Multiplicity Results for Homogeneous Second Order Differential Equations." Journal of Differential Equations 112, no. 1 (August 1994): 239–49. http://dx.doi.org/10.1006/jdeq.1994.1103.

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42

Maia, Lamiae, Noha El Khattabi, and Marlène Frigon. "Existence and multiplicity results for first-order Stieltjes differential equations." Advanced Nonlinear Studies 22, no. 1 (January 1, 2022): 684–710. http://dx.doi.org/10.1515/ans-2022-0038.

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Abstract In this article, we establish existence and multiplicity results for first-order Stieltjes differential equations satisfying a periodic boundary condition or an initial value condition. No monotonicity condition involving the right-hand side f f is imposed at the discontinuity points of the derivator g g . Our results rely on the fixed point index theory and new notions of strict lower and upper solutions. An application to a population model with an extreme event is presented to study the persistence of a species.

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43

Bagheri, M., and Ghasem A. Afrouzi. "Multiplicity results for Kirchhoff type elliptic problems with Hardy potential." Boletim da Sociedade Paranaense de Matemática 38, no. 4 (March 10, 2019): 31–50. http://dx.doi.org/10.5269/bspm.v38i4.36541.

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In this paper, we are concerned with the existence of solutions for fourth-order Kirchhoff type elliptic problems with Hardy potential. In fact, employing a consequence of the local minimum theorem due to Bonanno and mountain pass theorem we look into the existence results for the problem under algebraic conditions with the classical Ambrosetti-Rabinowitz (AR) condition on the nonlinear term. Furthermore, by combining two algebraic conditions on the nonlinear term using two consequences of the local minimum theorem due to Bonanno we ensure the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of third solution for our problem.

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44

Bonanno, Gabriele, and Giuseppina D'Aguì. "Multiplicity Results for a Perturbed Elliptic Neumann Problem." Abstract and Applied Analysis 2010 (2010): 1–10. http://dx.doi.org/10.1155/2010/564363.

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45

Wang, Libo, and Minghe Pei. "Existence Results for apx-Kirchhoff-Type Equation without Ambrosetti-Rabinowitz Condition." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/914210.

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We consider the existence and multiplicity of solutions for thepx-Kirchhoff-type equations without Ambrosetti-Rabinowitz condition. Using the Mountain Pass Lemma, the Fountain Theorem, and its dual, the existence of solutions and infinitely many solutions were obtained, respectively.

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46

Pucci, Patrizia. "Existence and multiplicity results for quasilinear equations in the Heisenberg group." Opuscula Mathematica 39, no. 2 (2019): 247–57. http://dx.doi.org/10.7494/opmath.2019.39.2.247.

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In this paper we complete the study started in [Existence of entire solutions for quasilinear equations in the Heisenberg group, Minimax Theory Appl. 4 (2019)] on entire solutions for a quasilinear equation \((\mathcal{E}_{\lambda})\) in \(\mathbb{H}^{n}\), depending on a real parameter \(\lambda\), which involves a general elliptic operator \(\mathbf{A}\) in divergence form and two main nonlinearities. Here, in the so called sublinear case, we prove existence for all \(\lambda\gt 0\) and, for special elliptic operators \(\mathbf{A}\), existence of infinitely many solutions \((u_k)_k\).

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47

Bonanno, Gabriele, Giuseppina Barletta, and Donal O’Regan. "A variational approach to multiplicity results for boundary-value problems on the real line." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 1 (January 30, 2015): 13–29. http://dx.doi.org/10.1017/s0308210513001200.

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We study the existence and multiplicity of solutions for a parametric equation driven by the p-Laplacian operator on unbounded intervals. Precisely, by using a recent local minimum theorem we prove the existence of a non-trivial non-negative solution to an equation on the real line, without assuming any asymptotic condition either at 0 or at ∞ on the nonlinear term. As a special case, we note the existence of a non-trivial solution for the problem when the nonlinear term is sublinear at 0. Moreover, under a suitable superlinear growth at ∞ on the nonlinearity we prove a multiplicity result for such a problem.

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48

Pei, Ruichang, and Jihui Zhang. "Existence and multiplicity results forp-laplacian Dirichlet problem with combined nonlinearities." Complex Variables and Elliptic Equations 59, no. 10 (January 3, 2014): 1475–88. http://dx.doi.org/10.1080/17476933.2013.856423.

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49

Mugnai, Dimitri, and Dayana Pagliardini. "Existence and multiplicity results for the fractional Laplacian in bounded domains." Advances in Calculus of Variations 10, no. 2 (April 1, 2017): 111–24. http://dx.doi.org/10.1515/acv-2015-0032.

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AbstractIn this paper, first we study existence results for a linearly perturbed elliptic problem driven by the fractional Laplacian. Then, we show a multiplicity result when the perturbation parameter is close to the eigenvalues. This latter result is obtained by exploiting the topological structure of the sublevels of the associated functional, which permits to apply a critical point theorem of mixed nature due to Marino and Saccon.

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50

Bereanu, C., and J. Mawhin. "Existence and multiplicity results for periodic solutions of nonlinear difference equations." Journal of Difference Equations and Applications 12, no. 7 (July 2006): 677–95. http://dx.doi.org/10.1080/10236190600654689.

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