Dirichlet problems with an indefinite and unbounded potential and concave-convex nonlinearities

Bibliographic description

punktacja MNiSW [2012 A]: 35

title:	Dirichlet problems with an indefinite and unbounded potential and concave-convex nonlinearities
author:	Gasiński Leszek , Papageorgiou Nikolaos S.
journal title:	Abstract and Applied Analysis
volume:	2012
date of publication :	2012
article ID:	492025
ISSN:	1085-3375
eISSN:	1687-0409
DOI:	10.1155/2012/492025
language:	English
journal language:	English
abstract in English:	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.
affiliation:	Wydział Matematyki i Informatyki : Katedra Teorii Optymalizacji i Sterowania
type:	journal article
subtype:	academic paper