Communications on Pure and Applied Analysis (CPAA)

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

Pages: 2487 - 2508, Volume 14, Issue 6, November 2015      doi:10.3934/cpaa.2015.14.2487

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Yinbin Deng - Department of Mathematics, Huazhong Normal University, Wuhan 430079, China (email)
Yi Li - Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, USA, United States (email)
Xiujuan Yan - Department of Mathematics, Huazhong Normal University, Wuhan, 430079, China, China (email)

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.

Keywords:  Quasilinear Schrödinger equations, radial solutions, nodal solutions.
Mathematics Subject Classification:  35J20, 35J62, 35Q55.

Received: June 2015;      Revised: June 2015;      Available Online: September 2015.