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2016 Infinitely many solutions for quasilinear Schrödinger equations under broken symmetry situation
Liang Zhang, Xianhua Tang, Yi Chen
Topol. Methods Nonlinear Anal. 48(2): 539-554 (2016). DOI: 10.12775/TMNA.2016.057

Abstract

In this paper, we study the existence of infinitely many solutions for the quasilinear Schrödinger equations $$ \begin{cases} -\Delta u-\Delta(|u|^{\alpha})|u|^{\alpha-2}u=g(x,u)+h(x,u) &\text{for } x\in \Omega,\\ u=0 &\text{for } x\in \partial\Omega, \end{cases} $$ where $\alpha\geq 2$, $g, h\in C(\Omega\times \mathbb{R}, \mathbb{R})$. When $g$ is of superlinear growth at infinity in $u$ and $h$ is not odd in $u$, the existence of infinitely many solutions is proved in spite of the lack of the symmetry of this problem, by using the dual approach and Rabinowitz perturbation method. Our results generalize some known results and are new even in the symmetric situation.

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Liang Zhang. Xianhua Tang. Yi Chen. "Infinitely many solutions for quasilinear Schrödinger equations under broken symmetry situation." Topol. Methods Nonlinear Anal. 48 (2) 539 - 554, 2016. https://doi.org/10.12775/TMNA.2016.057

Information

Published: 2016
First available in Project Euclid: 21 December 2016

zbMATH: 1362.35020
MathSciNet: MR3642772
Digital Object Identifier: 10.12775/TMNA.2016.057

Rights: Copyright © 2016 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.48 • No. 2 • 2016
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