# American Institute of Mathematical Sciences

July  2016, 15(4): 1309-1333. doi: 10.3934/cpaa.2016.15.1309

## Soliton solutions for a quasilinear Schrödinger equation with critical exponent

 1 Department of Mathematics, Central China Normal University, Wuhan, 430079, China 2 Department of Mathematics, Wuhan University of Technology, Wuhan, 430070, China

Received  October 2015 Revised  January 2016 Published  April 2016

This paper is concerned with the existence of soliton solutions for a quasilinear Schrödinger equation in $R^N$ with critical exponent, which appears from modelling the self-channeling of a high-power ultrashort laser in matter. By working with a perturbation approach which was initially proposed in [26], we prove that the given problem has a positive ground state solution.
Citation: Wentao Huang, Jianlin Xiang. Soliton solutions for a quasilinear Schrödinger equation with critical exponent. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1309-1333. doi: 10.3934/cpaa.2016.15.1309
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