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Existence results for nonlinear periodic boundary-value problems

Part of: Boundary value problems

Published online by Cambridge University Press:  02 February 2009

John R. Graef  and
Lingju Kong
John R. Graef
Affiliation:
Department of Mathematics, The University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA (john-graef@utc.edu, lingju-kong@utc.edu)
Lingju Kong
Affiliation:
Department of Mathematics, The University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA (john-graef@utc.edu, lingju-kong@utc.edu)
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Abstract

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We study a class of second-order nonlinear differential equations on a finite interval with periodic boundary conditions. The nonlinearity in the equations can take negative values and may be unbounded from below. Criteria are established for the existence of non-trivial solutions, positive solutions and negative solutions of the problems under consideration. Applications of our results to related eigenvalue problems are also discussed. Examples are included to illustrate some of the results. Our analysis relies mainly on topological degree theory.

Keywords

solutionsboundary-value problemsconespectral radiustopological degree

MSC classification

Secondary: 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 1 , February 2009 , pp. 79 - 95
Copyright
Copyright © Edinburgh Mathematical Society 2009