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

共 15 条

[1]

[Anonymous], 1996, ADV DIFFER EQU-NY

[2] A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics [J].

Badiale, M ;

Tarantello, G .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2002, 163 (04) :259-293

[3]

Badiale M, 2004, REV MAT IBEROAM, V20, P33

[4]

Badiale M., 2007, Adv. Differ. Equ, V12, P1321

[5]

Badiale M, 2007, J EUR MATH SOC, V9, P355

[6] ON SYMMETRICAL SOLUTIONS OF AN ELLIPTIC EQUATION WITH A NONLINEARITY INVOLVING CRITICAL SOBOLEV EXPONENT [J].

BIANCHI, G ;

CHABROWSKI, J ;

SZULKIN, A .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 25 (01) :41-59

[7] Elliptic equations with multi-singular inverse-square potentials and critical nonlinearity [J].

Felli, V ;

Terracini, S .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2006, 31 (03) :469-495

[8] Many-particle hardy inequalities [J].

Hoffmann-Stenhof, M. ;

Hoffmann-Ostenhof, T. ;

Laptev, A. ;

Tidblom, J. .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2008, 77 :99-114

[9]

Mazja V.G., 1985, Sobolev spaces

[10] Ground state solutions of a critical problem involving cylindrical weights [J].

Musina, Roberta .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (12) :3972-3986

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