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

[11] ELLIPTIC BOUNDARY-VALUE PROBLEMS WITH SINGULAR COEFFICIENTS AND CRITICAL NONLINEARITIES
EGNELL, H
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1989, 38 (02) : 235 - 251
[12] Gilbar D., 1983, ELLIPTIC PARTIAL DIF
[13] The role played by space dimension in elliptic critical problems
Jannelli, E
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 156 (02) : 407 - 426
[14] Lions P. L., 1985, Rev. Mat. Iberoam., V1, P145
[15] ON A NEUMANN PROBLEM WITH CRITICAL EXPONENT AND CRITICAL NONLINEARITY ON THE BOUNDARY
PIEROTTI, D
TERRACINI, S
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1995, 20 (7-8) : 1155 - 1187
[16] STRUWE M, 1984, MATH Z, V187, P511, DOI 10.1007/BF01174186
[17] Terracini S, 1996, ADV DIFF EQNS, V1, P241
[18] Yan S.S., 1995, CHINESE ANN MATH A, V16, P397

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