Soliton solutions for quasilinear Schrodinger equations:: The critical exponential case

被引：87
作者：
do O, Jodo M. B.
Miyagaki, Olimpio H. [1 ]
Soares, Sergio H. M.
机构：
[1] Univ Fed Vicosa, Dept Matemat, BR-36571000 Vicosa, MG, Brazil
[2] Univ Fed Paraiba, Dept Matemat, BR-58059900 Joao Pessoa, Paraiba, Brazil
[3] Univ Sao Paulo, ICMC USP, Dept Matemat, BR-13560970 Sao Carlos, SP, Brazil
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2007年 / 67卷 / 12期
关键词：
Trudinger-Moser inequality; elliptic equations; critical exponents; variational methods;
D O I：
10.1016/j.na.2006.10.018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Quasilinear elliptic equations in 1182 of second order with critical exponential growth are considered. By using a change of variable, the quasilinear equations are reduced to semilinear equations, whose respective associated functionals are well defined in H 1(12) and satisfy the geometric hypotheses of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle [P.L. Lions, The concentration compactness principle in the calculus of variations. The locally compact case. Part I and II, Ann. Inst. H. Poincare Anal. Non. Lineaire 1 (1984) 109-145, 223-283] combined with test functions connected with optimal Trudinger-Moser inequality. (c) 2006 Elsevier Ltd. All rights reserved.
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收藏
页码：3357 / 3372
页数：16
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