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MULTIPLE SOLUTIONS FOR A DIRICHLET PROBLEM WITH p-LAPLACIAN AND SET-VALUED NONLINEARITY

Part of: Elliptic equations and systems Existence theories

Published online by Cambridge University Press:  01 April 2008

D. AVERNA ,
S. A. MARANO  and
D. MOTREANU
D. AVERNA
Affiliation:
Dipartimento di Matematica ed Applicazioni, Università degli Studi di Palermo, Via Archirafi 34, 90123 Palermo, Italy (email: averna@math.unipa.it)
S. A. MARANO*
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italy (email: marano@dmi.unict.it)
D. MOTREANU
Affiliation:
Départment de Mathématiques, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan, France (email: motreanu@univ-perp.fr)
*
✉For correspondence; e-mail: marano@dmi.unict.it
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Abstract

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The existence of a negative solution, of a positive solution, and of a sign-changing solution to a Dirichlet eigenvalue problem with p-Laplacian and multi-valued nonlinearity is investigated via sub- and supersolution methods as well as variational techniques for nonsmooth functions.

Keywords

p-Laplaciangeneralized gradientmultiple nontrivial solutionssub- and supersolutionscritical points of nonsmooth functions

MSC classification

Secondary: 35J20: Variational methods for second-order elliptic equations 49J40: Variational methods including variational inequalities

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 2 , April 2008 , pp. 285 - 303
Copyright
Copyright © 2008 Australian Mathematical Society

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