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2000 Multiple solutions for nonlinear discontinuous strongly resonant elliptic problems
Nikolaos C. Kourogenis, Nikolaos S. Papageorgiou
Abstr. Appl. Anal. 5(2): 119-135 (2000). DOI: 10.1155/S1085337500000269


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.


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Nikolaos C. Kourogenis. Nikolaos S. Papageorgiou. "Multiple solutions for nonlinear discontinuous strongly resonant elliptic problems." Abstr. Appl. Anal. 5 (2) 119 - 135, 2000.


Published: 2000
First available in Project Euclid: 10 April 2003

zbMATH: 1007.35019
MathSciNet: MR1885326
Digital Object Identifier: 10.1155/S1085337500000269

Primary: 35J20

Rights: Copyright © 2000 Hindawi

Vol.5 • No. 2 • 2000
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