Nodal solutions for a quasilinear Schrödinger equation with criticalnonlinearity and non-square diffusion

Yinbin Deng; Yi  Li; Xiujuan  Yan

doi:10.3934/cpaa.2015.14.2487

Article Contents

2015, Volume 14, Issue 6: 2487-2508. Doi: 10.3934/cpaa.2015.14.2487

This issue Previous Article Global existence and blow up of solutions to a class of pseudo-parabolic equations with an exponential source Next Article Gaps in the spectrum of the Laplacian on $3N$-Gaskets

Nodal solutions for a quasilinear Schrödinger equation with critical nonlinearity and non-square diffusion

1.
Department of Mathematics, Huazhong Normal University, Wuhan 430079
2.
Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, USA
3.
Department of Mathematics, Huazhong Normal University, Wuhan, 430079, China

Received: May 31, 2015

Revised: May 31, 2015

Published: October 2015

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Abstract

This paper is concerned with a type of quasilinear Schrödinger equations of the form \begin{eqnarray} -\Delta u+V(x)u-p\Delta(|u|^{2p})|u|^{2p-2}u=\lambda|u|^{q-2}u+|u|^{2p2^{*}-2}u, \end{eqnarray} where $\lambda>0, N\ge3, 4p < q < 2p2^*, 2^*=\frac{2N}{N-2}, 1< p < +\infty$. For any given $k \ge 0$, by using a change of variables and Nehari minimization, we obtain a sign-changing minimizer with $k$ nodes.

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Mathematics Subject Classification: 35J20, 35J62, 35Q55.

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