Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities

Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities

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 multip...

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Main Authors: Leszek Gasiński, Nikolaos S. Papageorgiou
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/492025
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spelling doaj-456233036d094ff78ea285826204e4402020-11-24T23:20:34ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/492025492025Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex NonlinearitiesLeszek Gasiński0Nikolaos S. Papageorgiou1Faculty of Mathematics and Computer Science, Jagiellonian University, ulica Łojasiewicza 6, 30-348 Kraków, PolandDepartment of Mathematics, National Technical University, Zografou Campus, 15780 Athens, GreeceWe 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.http://dx.doi.org/10.1155/2012/492025
collection DOAJ
language English
format Article
sources DOAJ
author Leszek Gasiński
Nikolaos S. Papageorgiou
spellingShingle Leszek Gasiński
Nikolaos S. Papageorgiou
Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities
Abstract and Applied Analysis
author_facet Leszek Gasiński
Nikolaos S. Papageorgiou
author_sort Leszek Gasiński
title Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities
title_short Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities
title_full Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities
title_fullStr Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities
title_full_unstemmed Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities
title_sort dirichlet problems with an indefinite and unbounded potential and concave-convex nonlinearities
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description 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.
url http://dx.doi.org/10.1155/2012/492025
work_keys_str_mv AT leszekgasinski dirichletproblemswithanindefiniteandunboundedpotentialandconcaveconvexnonlinearities
AT nikolaosspapageorgiou dirichletproblemswithanindefiniteandunboundedpotentialandconcaveconvexnonlinearities
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