Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Multiple solutions for strongly resonant nonlinear elliptic problems with discontinuities

Author(s): Sophia Th. Kyritsi; Nikolaos S. Papageorgiou
Journal: Proc. Amer. Math. Soc. 133 (2005), 2369-2376.
MSC (2000): Primary 35J20, 35J60, 35R05
Posted: March 15, 2005
MathSciNet review: 2138879
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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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