A variational approach to multiplicity results for boundary-value problems on the real line. Issue 1 (30th January 2015)

• Record Type: Journal Article
• Authors: Bonanno, Gabriele; Barletta, Giuseppina; O'Regan, Donal
• Is Part Of: Proceedings. Volume 145:Issue 1(2015)
• Page Start: 13
• Page End: 29
• Publication Date: 2015-01-30
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210513001200
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : We study the existence and multiplicity of solutions for a parametric equation driven by the p -Laplacian operator on unbounded intervals. Precisely, by using a recent local minimum theorem we prove the existence of a non-trivial non-negative solution to an equation on the real line, without assuming any asymptotic condition either at 0 or at ∞ on the nonlinear term. As a special case, we note the existence of a non-trivial solution for the problem when the nonlinear term is sublinear at 0. Moreover, under a suitable superlinear growth at ∞ on the nonlinearity we prove a multiplicity result for such a problem.