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Positive solutions and multiple solutions at non-resonance, resonance and near resonance for hemivariational inequalities with $ p$-Laplacian


Authors: D. Motreanu, V. V. Motreanu and N. S. Papageorgiou
Journal: Trans. Amer. Math. Soc. 360 (2008), 2527-2545
MSC (2000): Primary 35J20, 35R70; Secondary 35J60, 35J85.
DOI: https://doi.org/10.1090/S0002-9947-07-04449-2
Published electronically: December 11, 2007
MathSciNet review: 2373324
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Abstract: In this paper we study eigenvalue problems for hemivariational inequalities driven by the $ p$-Laplacian differential operator. We prove the existence of positive smooth solutions for both non-resonant and resonant problems at the principal eigenvalue of the negative $ p$-Laplacian with homogeneous Dirichlet boundary condition. We also examine problems which are near resonance both from the left and from the right of the principal eigenvalue. For nearly resonant from the right problems we also prove a multiplicity result.


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Additional Information

D. Motreanu
Affiliation: Département de Mathématiques, Université de Perpignan, 66860 Perpignan, France
Email: motreanu@univ-perp.fr

V. V. Motreanu
Affiliation: Département de Mathématiques, Université de Perpignan, 66860 Perpignan, France
Email: viorica@univ-perp.fr

N. S. Papageorgiou
Affiliation: Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
Email: npapg@math.ntua.gr

DOI: https://doi.org/10.1090/S0002-9947-07-04449-2
Keywords: Hemivariational inequality, eigenvalue problem, resonance
Received by editor(s): February 14, 2006
Published electronically: December 11, 2007
Article copyright: © Copyright 2007 American Mathematical Society

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