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

Published online by Cambridge University Press:  30 March 2011

Abdulkadir Dogan
Affiliation:
Nigde Universitesi, Fen Edebiyat Fakultesi, Matematik Bolumu, Ogretim Uyesi, 51100 Nigde, Turkey (abdulkadir94@hotmail.com)
John R. Graef
Affiliation:
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA (john-graef@utc.edu; lingju-kong@utc.edu)
Lingju Kong
Affiliation:
Department of Mathematics, 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 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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2011

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