On a class of singular biharmonic problems involving critical exponents

被引：29

作者：

Alves, CO

do O, JM ^{[1
]}

Miyagaki, OH

机构：

[1] Univ Fed Paraiba, Dept Matemat, BR-58059900 Joao Pessoa, Paraiba, Brazil

[2] Univ Fed Paraiba, Dept Matemat & Estatist, BR-58109970 Campina Grande, PB, Brazil

[3] Univ Fed Vicosa, Dept Matemat, BR-36571000 Vicosa, MG, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2003年 / 277卷 / 01期

关键词：

biharmonic operator; critical Sobolev exponents; hardy inequality; singular and indefinite potential;

D O I：

10.1016/S0022-247X(02)00283-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the following class of singular biharmonic problems [GRAPHICS] where 1 less than or equal to q < 2* -1, 2* = 2N/(N-4) is the critical Sobolev exponent, Delta(2) denotes the biharmonic operator, Omega is open domain (not necessarily bounded, it may be equal to R-N) and V is a potential that changes sign in Omega with some points of singularities in Omega. Some results on the existence of solutions are obtained by combining the Mountain Pass Theorem and Hardy inequality with some arguments used by Brezis and Nirenberg. (C) 2002 Elsevier Science (USA). All rights reserved.

引用

页码：12 / 26

页数：15

共 25 条

[1] Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7
[2] [Anonymous], 1996, ADV DIFF EQU
[3] MULTIPLICITY OF SOLUTIONS FOR ELLIPTIC PROBLEMS WITH CRITICAL EXPONENT OR WITH A NONSYMMETRIC TERM
AZORERO, JG
ALONSO, IP
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 323 (02) : 877 - 895
[4] AZORERO JG, 1997, HARDY INEQUALITIES S
[5] EXISTENCE OF POSITIVE SOLUTIONS OF THE EQUATION -DELTA-U+A(X)U=U(N+2)/(N-2) IN RN
BENCI, V
CERAMI, G
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1990, 88 (01) : 90 - 117
[6] Extrema problems with critical Sobolev exponents on unbounded domains
BenNaoum, AK
Troestler, C
Willem, M
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1996, 26 (04) : 823 - 833
[7] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS
BREZIS, H
NIRENBERG, L
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) : 437 - 477
[8] A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS
BREZIS, H
LIEB, E
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) : 486 - 490
[9] CAFFARELLI L, 1984, COMPOS MATH, V53, P259
[10] Carriao P. C., 1998, DIFFERENTIAL INTEGRA, V11, P61

← 1 2 3 →