GROUND STATE SOLUTIONS FOR A SEMILINEAR PROBLEM WITH CRITICAL EXPONENT

被引：0

作者：

Szulkin, Andrzej ^{[1
]}

Weth, Tobias ^{[2
]}

Willem, Michel ^{[3
]}

机构：

[1] Stockholm Univ, Dept Math, S-10691 Stockholm, Sweden

[2] Goethe Univ Frankfurt, Inst Math, D-60054 Frankfurt, Germany

[3] Catholic Univ Louvain, Dept Math, B-1348 Louvain, Belgium

来源：

DIFFERENTIAL AND INTEGRAL EQUATIONS | 2009年 / 22卷 / 9-10期

关键词：

CRITICAL SOBOLEV EXPONENTS; NONLINEAR ELLIPTIC PROBLEMS; NODAL SOLUTIONS; EQUATIONS; SYMMETRY; DOMAINS; SYSTEM;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work is devoted to the existence and qualitative properties of ground state solutions of the Dirchlet problem for the semilinear equation -Delta u - lambda u = |u|(2)*(-2)u in a bounded domain. Here, 2* is the critical Sobolev exponent, and the term ground state refers to minimizers of the corresponding energy within the set of nontrivial solutions. We focus on the indefinite case where A is larger than the first Dirichlet eigenvalue of the Laplacian, and we present a particularly simple approach to the study of ground states.

引用

页码：913 / 926

页数：14

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