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

被引：28
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.
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页码：4213 / 4230
页数：18
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