Soliton solutions for a quasilinear Schrödinger equation with critical exponent

Wentao  Huang; Jianlin  Xiang

doi:10.3934/cpaa.2016.15.1309

Article Contents

2016, Volume 15, Issue 4: 1309-1333. Doi: 10.3934/cpaa.2016.15.1309

This issue Previous Article The Nehari manifold for fractional systems involving critical nonlinearities Next Article Higher integrability of weak solution of a nonlinear problem arising in the electrorheological fluids

Soliton solutions for a quasilinear Schrödinger equation with critical exponent

Wentao Huang^1, and
Jianlin Xiang^2,

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

Received: September 30, 2015

Revised: December 31, 2015

Published: June 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J62; Secondary: 35B09, 35B33.

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