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Open Access Open Badges Research Article

Multiple Positive Solutions for m-Point Boundary Value Problem on Time Scales

Jie Liu12 and Hong-Rui Sun2*

Author Affiliations

1 Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, China

2 School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, China

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Boundary Value Problems 2011, 2011:591219  doi:10.1155/2011/591219

Published: 10 August 2010


The purpose of this article is to establish the existence of multiple positive solutions of the dynamic equation on time scales , subject to the multi-point boundary condition , where is an increasing homeomorphism and satisfies the relation for , which generalizes the usually p-Laplacian operator. An example applying the result is also presented. The main tool of this paper is a generalization of Leggett-Williams fixed point theorem, and the interesting points are that the nonlinearity f contains the first-order derivative explicitly and the operator is not necessarily odd.