Abstract and Applied Analysis

Multiple solutions for nonlinear discontinuous strongly resonant elliptic problems

Nikolaos C. Kourogenis and Nikolaos S. Papageorgiou

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Abstract

We consider quasilinear strongly resonant problems with discontinuous right-hand side. To develop an existence theory we pass to a multivalued problem by, roughly speaking, filling in the gaps at the discontinuity points. We prove the existence of at least three nontrivial solutions. Our approach uses the nonsmooth critical point theory for locally Lipschitz functionals due to Chang (1981) and a generalized version of the Ekeland variational principle. At the end of the paper we show that the nonsmooth Palais-Smale (PS)-condition implies the coercivity of the functional, extending this way a well-known result of the “smooth” case.

Article information

Source
Abstr. Appl. Anal., Volume 5, Number 2 (2000), 119-135.

Dates
First available in Project Euclid: 10 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049999287

Digital Object Identifier
doi:10.1155/S1085337500000269

Mathematical Reviews number (MathSciNet)
MR1885326

Zentralblatt MATH identifier
1007.35019

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations

Citation

Kourogenis, Nikolaos C.; Papageorgiou, Nikolaos S. Multiple solutions for nonlinear discontinuous strongly resonant elliptic problems. Abstr. Appl. Anal. 5 (2000), no. 2, 119--135. doi:10.1155/S1085337500000269. https://projecteuclid.org/euclid.aaa/1049999287


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