Standing waves with a critical frequency for a quasilinear Schrödinger equation

Author:

Fang Xiang-Dong1

Affiliation:

1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China

Abstract

We consider the following quasilinear Schrödinger equation [Formula: see text] where [Formula: see text], [Formula: see text], and [Formula: see text] satisfies a weaker growth condition than the Ambrosetti–Rabinowitz type condition in Byeon and Wang [Standing waves with a critical frequency for nonlinear Schrödinger equations, Arch. Ration. Mech. Anal. 165(4) (2002) 295–316; Standing waves with a critical frequency for nonlinear Schrödinger equations, II, Calc. Var. 18(2) (2003) 207–219]. We obtain the existence of the localized bound state solutions concentrating at an isolated component of the local minimum of [Formula: see text] and whose amplitude goes to 0 as [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

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