Dirichlet Problems with an Indefinite and Unbounded Potential and Concave-Convex Nonlinearities. (6th June 2012)

• Record Type: Journal Article
• Authors: Gasiński, Leszek; Papageorgiou, Nikolaos S.
• Other Names: Rogovchenko Yuriy Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-06-06
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/492025
• Languages: English
• ISSNs: 1085-3375

Abstract

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.