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 ( (uΔ(t))) +h(t)f(t,u(t),uΔ(t))=0, t∈(0,T)T, subject to the multi-point boundary condition uΔ(0)=0, u(T)=∑i=1m 2aiu(ξi), where : → is an increasing homeomorphism and satisfies the relation (xy)= (x) (y) for x,y∈ , 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.