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2012 Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities
Leszek Gasiński, Nikolaos S. Papageorgiou
Abstr. Appl. Anal. 2012(SI09): 1-36 (2012). DOI: 10.1155/2012/492025

Abstract

We consider a parametric semilinear Dirichlet problem with an unbounded and indefinite potential. In the reaction we have the competing effects of a sublinear (concave) term and of a superlinear (convex) term. Using variational methods coupled with suitable truncation techniques, we prove two multiplicity theorems for small values of the parameter. Both theorems produce five nontrivial smooth solutions, and in the second theorem we provide precise sign information for all the solutions.

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Leszek Gasiński. Nikolaos S. Papageorgiou. "Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities." Abstr. Appl. Anal. 2012 (SI09) 1 - 36, 2012. https://doi.org/10.1155/2012/492025

Information

Published: 2012
First available in Project Euclid: 1 April 2013

zbMATH: 1246.35075
MathSciNet: MR2926910
Digital Object Identifier: 10.1155/2012/492025

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI09 • 2012
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