SCHRODINGER EQUATION WITH MULTIPARTICLE POTENTIAL AND CRITICAL NONLINEARITY

被引：0

作者：

Chabrowski, Jan ^{[1
]}

Szulkin, Andrzej ^{[2
]}

Willem, Michel ^{[3
]}

机构：

[1] Univ Queensland, Dept Math, Brisbane, Qld 4072, Australia

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

[3] Univ Catholique Louvain, Inst Math Pure & Appl, B-1348 Louvain, Belgium

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2009年 / 34卷 / 02期

关键词：

Schrodinger equation; multiparticle potential; Hardy inequality; ground state; concentration-compactness; ELLIPTIC EQUATION; INEQUALITY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the existence and non-existence of ground states for the Schrodinger equations -Delta u - lambda Sigma(i<j) u/vertical bar x(i) - x(j)vertical bar(2) = vertical bar u vertical bar(2)* -(2)u, x = (x(1), ... , x(m)) is an element of R-mN, and -Delta u -lambda u/vertical bar y vertical bar(2) = vertical bar u vertical bar(2*) (-2)u, x = (y, z) is an element of R-N. In both cases we assume lambda not equal 0 and lambda < (lambda) over bar, where (lambda) over bar is the Hardy constant corresponding to the problem.

引用

页码：201 / 211

页数：11