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Non-trivial solutions of local and non-local Neumann boundary-value problems

Part of: Nonlinear operators and their properties Boundary value problems

Published online by Cambridge University Press:  07 March 2016

Gennaro Infante ,
Paolamaria Pietramala  and
F. Adrián F. Tojo
Gennaro Infante
Affiliation:
Dipartimento di Matematica e Informatica, Università della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy (gennaro.infante@unical.it; pietramala@unical.it)
Paolamaria Pietramala
Affiliation:
Dipartimento di Matematica e Informatica, Università della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy (gennaro.infante@unical.it; pietramala@unical.it)
F. Adrián F. Tojo
Affiliation:
Departamento de Análise Matemática, Facultade de Matematicás, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain (fernandoadrian.fernandez@usc.es)
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Extract

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.

Keywords

fixed-point indexconenon-trivial solutionNeumann conditions

MSC classification

Primary: 34B10: Nonlocal and multipoint boundary value problems
Secondary: 34B18: Positive solutions of nonlinear boundary value problems 34B27: Green functions 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 2 , April 2016 , pp. 337 - 369
Copyright
Copyright © Royal Society of Edinburgh 2016 

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