Nodal solutions for a generalized quasilinear Schrödinger equation with critical exponents

Kun Cheng; Yinbin Deng

doi:10.3934/dcds.2017004

Article Contents

2017, Volume 37, Issue 1: 77-103. Doi: 10.3934/dcds.2017004

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Nodal solutions for a generalized quasilinear Schrödinger equation with critical exponents

Kun Cheng and
Yinbin Deng

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

Received: February 29, 2016

Revised: March 31, 2016

Published: September 2017

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)

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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 $k ≥ 0$.

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Mathematics Subject Classification: Primary:35Q55;Secondary:35J62, 35J20.

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