POSITIVE GROUND STATE SOLUTIONS FOR A QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL EXPONENT

被引：29

作者：

Deng, Yinbin ^{[1
]}

Huang, Wentao ^{[1
]}

机构：

[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 08期

关键词：

Ground state solutions; quasilinear elliptic equation; critical exponent; NONLINEAR SCHRODINGER-EQUATION; CONCENTRATION-COMPACTNESS PRINCIPLE; SOLITON-SOLUTIONS; CRITICAL GROWTH; R-N; EXISTENCE; PLASMA;

D O I：

10.3934/dcds.2017179

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the following quasilinear elliptic equation with critical Sobolev exponent: -Delta u + V(x)u - [Delta(1 + u(2))(1/2)]u/2(1+u(2))(1/2) = |u|(2*-2)u + |u|(p-2)u, x is an element of R-N, which models the self-channeling of a high-power ultra short laser in matter, where N >= 3, 2 < p < 2* - 2N/N-2 and V(x) is a given positive potential. Combining the change of variables and an abstract result developed by Jeanjean in [14], we obtain the existence of positive ground state solutions for the given problem.

引用

页码：4213 / 4230

页数：18

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