Three nontrivial solutions for a quasilinear elliptic differential equation at resonance with discontinuous right hand side

被引：8

作者：

Kourogenis, NC ^{[1
]}

Papageorgiou, NS ^{[1
]}

机构：

[1] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 1999年 / 238卷 / 02期

关键词：

p-Laplacian; nonsmooth Palais-Smale condition; locally Lipschitz function; generalized subdifferential; critical point; nonsmooth mountain pass theorem; coercive functional; Ekeland variational principle; local minimum;

D O I：

10.1006/jmaa.1999.6526

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a quasilinear elliptic equation at resonance with discontinuous right hand side. To have an existence theory, we pass to a multivalued version of the problem by filling in the gaps at the discontinuity points. Using the nonsmooth critical point theory of Chang for locally Lipschitz functionals and the Ekeland variational principle, we show that the resulting elliptic inclusion has three distinct nontrivial solutions. (C) 1999 Academic Press.

引用

页码：477 / 490

页数：14

共 21 条

[1]

Adams A, 2003, SOBOLEV SPACES

[2] MULTIPLE NONTRIVIAL SOLUTIONS OF RESONANT AND NONRESONANT ASYMPTOTICALLY LINEAR-PROBLEMS [J].

AHMAD, S .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 96 (03) :405-409

[3] ELEMENTARY CRITICAL-POINT THEORY AND PERTURBATIONS OF ELLIPTIC BOUNDARY-VALUE PROBLEMS AT RESONANCE [J].

AHMAD, S ;

LAZER, AC ;

PAUL, JL .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1976, 25 (10) :933-944

[4]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[5] ABSTRACT CRITICAL-POINT THEOREMS AND APPLICATIONS TO SOME NON-LINEAR PROBLEMS WITH STRONG RESONANCE AT INFINITY [J].

BARTOLO, P ;

BENCI, V ;

FORTUNATO, D .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (09) :981-1012

[6]

Brezis H., 1983, ANAL FONCTIONELLE

[7] VARIATIONAL-METHODS FOR NON-DIFFERENTIABLE FUNCTIONALS AND THEIR APPLICATIONS TO PARTIAL-DIFFERENTIAL EQUATIONS [J].

CHANG, KC .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1981, 80 (01) :102-129

[8]

Clarke FH, 1983, OPTIMIZATION NONSMOO

[9]

DIAZ IJ, 1985, PITMAN RES NOTES MAT, V106

[10] MULTIPLE NONTRIVIAL SOLUTIONS OF SEMILINEAR STRONGLY RESONANT ELLIPTIC-EQUATIONS [J].

GONCALVES, JVA ;

MIYAGAKI, OH .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1992, 19 (01) :43-52

← 1 2 3 →