Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 252876, 13 pages
doi:10.1155/2008/252876
Several Existence Theorems of Nonlinear m-Point BVP for an Increasing Homeomorphism and Homomorphism on Time Scales
Yanbin Sang1
, Hua Su2
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
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.