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

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.