Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 189768, 12 pages
Research Article

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

Department of Mathematics, Shanxi Datong University, Datong, Shanxi 037009, China

Received 27 August 2008; Revised 24 November 2008; Accepted 14 January 2009

Academic Editor: Binggen Zhang

Copyright © 2009 Ying Zhang and ShiDong Qiao. 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.


We study the one-dimensional p-Laplacian m-point boundary value problem (φp(uΔ(t)))Δ+a(t)f(t,u(t))=0, t[0,1]T, u(0)=0, u(1)=i=1m2aiu(ξi), where T is a time scale, φp(s)=|s|p2s, 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 Krasnoselsklls 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.