Several Existence Theorems of Multiple Positive Solutions of Nonlinear http://static-content.springer.com/image/art%3A10.1155%2F2009%2F584145/MediaObjects/13661_2009_Article_863_IEq1_HTML.gif -Point BVP for an Increasing Homeomorphism and Homomorphism on Time Scales

Boundary Value Problems20092009:584145

DOI: 10.1155/2009/584145

Received: 24 July 2009

Accepted: 29 November 2009

Published: 7 December 2009

Abstract

By using fixed point theorems in cones, the existence of multiple positive solutions is considered for nonlinear http://static-content.springer.com/image/art%3A10.1155%2F2009%2F584145/MediaObjects/13661_2009_Article_863_IEq2_HTML.gif -point boundary value problem for the following second-order boundary value problem on time scales http://static-content.springer.com/image/art%3A10.1155%2F2009%2F584145/MediaObjects/13661_2009_Article_863_IEq3_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2009%2F584145/MediaObjects/13661_2009_Article_863_IEq4_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2009%2F584145/MediaObjects/13661_2009_Article_863_IEq5_HTML.gif , http://static-content.springer.com/image/art%3A10.1155%2F2009%2F584145/MediaObjects/13661_2009_Article_863_IEq6_HTML.gif , where http://static-content.springer.com/image/art%3A10.1155%2F2009%2F584145/MediaObjects/13661_2009_Article_863_IEq7_HTML.gif is an increasing homeomorphism and homomorphism and http://static-content.springer.com/image/art%3A10.1155%2F2009%2F584145/MediaObjects/13661_2009_Article_863_IEq8_HTML.gif . Some new results are obtained for the existence of twin or an arbitrary odd number of positive solutions of the above problem by applying Avery-Henderson and Leggett-Williams fixed point theorems, respectively. In particular, our criteria generalize and improve some known results by Ma and Castaneda (2001). We must point out for readers that there is only the http://static-content.springer.com/image/art%3A10.1155%2F2009%2F584145/MediaObjects/13661_2009_Article_863_IEq9_HTML.gif -Laplacian case for increasing homeomorphism and homomorphism. As an application, one example to demonstrate our results is given.

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Authors’ Affiliations

(1)
Department of Mathematics, North University of China
(2)
Institute of Applied Mathematics, Shanxi Datong University

Copyright

© W. Han and S. Kang. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.