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Positive solutions of a nonlinear Sturm–Liouville boundary-value problem

Part of: Boundary value problems Elliptic equations and systems

Published online by Cambridge University Press:  23 September 2009

Patricio Cerda  and
Pedro Ubilla
Patricio Cerda
Affiliation:
Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile; Email: ([email protected], [email protected])
Pedro Ubilla
Affiliation:
Departamento de Matemática y Ciencia de la Computación, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile; Email: ([email protected], [email protected])
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Abstract

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We establish the existence of positive solutions of the Sturm–Liouville problem

where

We assume g and to be non-negative, continuous functions, a(s) is a positive continuous function, c≥0, p>1, and the function h is sub-quadratic with respect to u′. We combine a priori estimates with a fixed-point result of Krasnosel'skii to obtain the existence of a positive solution.

Keywords

Sturm–Liouville problemspositive solutionsfixed pointstopological degree

MSC classification

Secondary: 35J65: Nonlinear boundary value problems for linear elliptic equations 34B15: Nonlinear boundary value problems 34B18: Positive solutions of nonlinear boundary value problems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 3 , October 2009 , pp. 561 - 568
Copyright
Copyright © Edinburgh Mathematical Society 2009