Existence of Positive Solutions for m-Point Boundary Value Problems on Time Scales

We study the one-dimensional p-Laplacian m-point boundary value problem (phi(p)(u(Delta)(t)))(Delta) + a(t)f(t, u(t)) = 0, t is an element of [0, 1](T), u(0) = 0, u(1) = Sigma(m-2)(i=1)a(i)u(xi(i)), where T is a time scale, phi(p)(s) = vertical bar s vertical bar(p-2)s, p > 1, some new results are obtained for the existence of at least one, two, and three positive solution/solutions of the above problem by using Krasnosel' skll's fixed point theorem, new fixed point theorem due to Avery and Henderson, as well as Leggett-Williams fixed point theorem. This is probably the first time the existence of positive solutions of one-dimensional p-Laplacian m-point boundary value problem on time scales has been studied. Copyright (c) 2009 Y. Zhang and S. Qiao.