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January  2017, 37(1): 77-103. doi: 10.3934/dcds.2017004

## Nodal solutions for a generalized quasilinear Schrödinger equation with critical exponents

 Department of Mathematics, Huazhong Normal University, Wuhan 430079, China

Received  March 2016 Revised  April 2016 Published  November 2016

Fund Project: This work was supported by the Natural Science Foundation of China (11371160,11328101) and the Program for Changjiang Scholars and Innovative Research Team in University (#IRT13066).

This paper is concerned with constructing nodal radial solutions for generalized quasilinear Schrödinger equations in $\mathbb{R}^N$ with critical growth which arise from plasma physics, fluid mechanics, as well as the self-channeling of a high-power ultashort laser in matter. We find the critical exponents for a generalized quasilinear Schrödinger equations and obtain the existence of sign-changing solution with k nodes for any given integer $k ≥ 0$.

Citation: Kun Cheng, Yinbin Deng. Nodal solutions for a generalized quasilinear Schrödinger equation with critical exponents. Discrete & Continuous Dynamical Systems, 2017, 37 (1) : 77-103. doi: 10.3934/dcds.2017004
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