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Hemivariational inequalities with the potential crossing the first eigenvalue

Published online by Cambridge University Press:  17 April 2009

Sophia Th. Kyritsi  and
Nikolaos S. Papageorgiou
Sophia Th. Kyritsi
Affiliation:
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece
Nikolaos S. Papageorgiou
Affiliation:
National Technical University, Department of Mathematics, Zografou Campus, Athens 157 80, Greece e-mail:npapg@math.ntua.gr
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Abstract

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In this paper we study a nonlinear hemivariational inequality involving the p-Laplacian. Our approach is variational and uses a recent nonsmooth Linking Theorem, due to Kourogenis and Papageorgiou (2000). The use of the Linking Theorem instead of the Mountain Pass Theorem allows us to assume an asymptotic behaviour of the generalised potential function which goes beyond the principal eigenvalue of the negative p-Laplacian with Dirichlet boundary conditions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 3 , December 2001 , pp. 381 - 393
Copyright
Copyright © Australian Mathematical Society 2001

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