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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Multiple solutions for strongly resonant nonlinear elliptic problems with discontinuities


Authors: Sophia Th. Kyritsi and Nikolaos S. Papageorgiou
Journal: Proc. Amer. Math. Soc. 133 (2005), 2369-2376
MSC (2000): Primary 35J20, 35J60, 35R05
Published electronically: March 15, 2005
MathSciNet review: 2138879
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Abstract: We examine a nonlinear strongly resonant elliptic problem driven by the $p$-Laplacian and with a discontinuous nonlinearity. We assume that the discontinuity points are countable and at them the nonlinearity has an upward jump discontinuity. We show that the problem has at least two nontrivial solutions without using a multivalued interpretation of the problem as it is often the case in the literature. Our approach is variational based on the nonsmooth critical point theory for locally Lipschitz functions.


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Additional Information

Sophia Th. Kyritsi
Affiliation: Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece

Nikolaos S. Papageorgiou
Affiliation: Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07864-0
PII: S 0002-9939(05)07864-0
Keywords: $p$-Laplacian, strong resonance, nonsmooth critical point theory, generalized subdifferential, multiple solutions, discontinuous nonlinearity, generalized Ekeland variational principle
Received by editor(s): January 13, 2004
Published electronically: March 15, 2005
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2005 American Mathematical Society