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Higher-order singular multi-point boundary-value problems on time scales

Part of: Boundary value problems

Published online by Cambridge University Press:  30 March 2011

Abdulkadir Dogan ,
John R. Graef  and
Lingju Kong
Abdulkadir Dogan
Affiliation:
Nigde Universitesi, Fen Edebiyat Fakultesi, Matematik Bolumu, Ogretim Uyesi, 51100 Nigde, Turkey ([email protected])
John R. Graef
Affiliation:
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA ([email protected]; [email protected])
Lingju Kong
Affiliation:
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA ([email protected]; [email protected])
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Abstract

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We study classes of higher-order singular boundary-value problems on a time scale with a positive parameter λ in the differential equations. A homeomorphism and homomorphism ø are involved both in the differential equation and in the boundary conditions. Criteria are obtained for the existence and uniqueness of positive solutions. The dependence of positive solutions on the parameter λ is studied. Applications of our results to special problems are also discussed. Our analysis mainly relies on the mixed monotone operator theory. The results here are new, even in the cases of second-order differential and difference equations.

Keywords

positive solutionssingular boundary-value problemsexistenceuniquenessdependencemixed monotone operator

MSC classification

Secondary: 34B15: Nonlinear boundary value problems 34B08: Parameter dependent boundary value problems 34B10: Nonlocal and multipoint boundary value problems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 2 , June 2011 , pp. 345 - 361
Copyright
Copyright © Edinburgh Mathematical Society 2011

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