A global compactness result for singular elliptic problems involving critical Sobolev exponent

被引：66

作者：

Cao, DM ^{[1
]}

Peng, SJ

机构：

[1] Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China

[2] Xiao Gan Univ, Dept Math, Xiao Gan, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2003年 / 131卷 / 06期

关键词：

Palais-Smale sequence; compactness; Sobolev and Hardy critical exponents;

D O I：

10.1090/S0002-9939-02-06729-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Omega subset of R-N be a bounded domain such that 0 is an element of Omega, N greater than or equal to 3, 2* = 2N/N-2, lambda is an element of R, epsilon is an element of R. Let {u(n)} subset of H-0(1)(Omega) be a (P.S.) sequence of the functional E-lambda,E-epsilon(u) = 1/2 integral(Omega)(\delu\(2) - lambdau(2) / \x\(2) - epsilonu(2)) - 1/2* integral(Omega)\u\(2*). We study the limit behaviour of un and obtain a global compactness result.

引用

页码：1857 / 1866

页数：10

共 18 条

[1] Global compactness properties of semilinear elliptic equations with critical exponential growth [J].

Adimurthi ;

Struwe, M .

JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 175 (01) :125-167

[2]

Azorero JPG, 1998, J DIFFER EQUATIONS, V144, P441

[3] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].

BREZIS, H ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) :437-477

[4] A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS [J].

BREZIS, H ;

LIEB, E .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) :486-490

[5]

Catrina F., 2000, COMMUN PUR APPL MATH, V53, P1, DOI [10.1002/(SICI)1097-0312(200001)53:13.0.CO

[6]

2-U, DOI 10.1002/(SICI)1097-0312(200001)53:13.0.CO

[7]

2-U]

[8] ON THE BEST CONSTANT FOR A WEIGHTED SOBOLEV-HARDY INEQUALITY [J].

CHOU, KS ;

CHU, CW .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1993, 48 :137-151

[9]

CORON JM, 1984, CR ACAD SCI I-MATH, V299, P209

[10]

Ding W., 1989, J. Partial Differ. Equ., V2, P83

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