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 | References | Similar Articles | Additional Information

Abstract: We examine a nonlinear strongly resonant elliptic problem driven by the -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

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