Non-trivial solutions of local and non-local Neumann boundary-value problems. Issue 2 (7th March 2016)

• Record Type: Journal Article
• Authors: Infante, Gennaro; Pietramala, Paolamaria; F. Tojo, F. Adrián
• Is Part Of: Proceedings. Volume 146:Issue 2(2016)
• Page Start: 337
• Page End: 369
• Publication Date: 2016-03-07
• Subjects: fixed-point index, -- cone, -- non-trivial solution, -- Neumann conditions; Primary 34B10, -- Secondary 34B18, -- 34B27, -- 47H30; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210515000499
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : We prove new results on the existence, non-existence, localization and multiplicity of non-trivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed-point index. Some of the criteria involve a comparison with the spectral radius of some related linear operators. We apply our results to some boundary-value problems with local and non-local boundary conditions of Neumann type. We illustrate in some examples the methodologies used.