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Media type:
E-Article
Title:
Positive solutions and multiple solutions at non-resonance, resonance and near resonance for hemivariational inequalities with ๐-Laplacian
Contributor:
Motreanu, D.;
Motreanu, V.;
Papageorgiou, N.
imprint:
American Mathematical Society (AMS), 2007
Published in:Transactions of the American Mathematical Society
Language:
English
DOI:
10.1090/s0002-9947-07-04449-2
ISSN:
0002-9947;
1088-6850
Origination:
Footnote:
Description:
<p>In this paper we study eigenvalue problems for hemivariational inequalities driven by the<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"><mml:semantics><mml:mi>p</mml:mi><mml:annotation encoding="application/x-tex">p</mml:annotation></mml:semantics></mml:math></inline-formula>-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<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p"><mml:semantics><mml:mi>p</mml:mi><mml:annotation encoding="application/x-tex">p</mml:annotation></mml:semantics></mml:math></inline-formula>-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.</p>