Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 252876, 13 pages
doi:10.1155/2008/252876
Research Article

Several Existence Theorems of Nonlinear m-Point BVP for an Increasing Homeomorphism and Homomorphism on Time Scales

Yanbin Sang,1 Hua Su,2 and Yafeng Xiao1

1Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China
2School of Information Science and Technology, Shandong University of Science and Technology, Qingdao, Shandong 266510, China

Received 20 January 2008; Accepted 26 March 2008

Academic Editor: Bing Zhang

Copyright © 2008 Yanbin Sang et al. 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.

Abstract

Several existence theorems of positive solutions are established for nonlinear m-point boundary value problem for the following dynamic equations on time scales (ϕ(uΔ))∇+a(t)f(t,u(t))=0, t∈(0,T), ϕ(uΔ(0))=∑i=1m−2aiϕ(uΔ(ξi)), u(T)=∑i=1m−2biu(ξi), where ϕ:R→R is an increasing homeomorphism and homomorphism and ϕ(0)=0. As an application, an example to demonstrate our results is given.