Advances in Difference Equations
Volume 2009 (2009), Article ID 209707, 18 pages
doi:10.1155/2009/209707
Research Article

Existence Results for Higher-Order Boundary Value Problems on Time Scales

Jian Liu1 and Yanbin Sang2

1School of Mathematics and Statistics, Shandong Economics University, Jinan Shandong 250014, China
2Department of Mathematics, North University of China, Taiyuan Shanxi 030051, China

Received 22 March 2009; Revised 5 June 2009; Accepted 16 June 2009

Academic Editor: Victoria Otero-Espinar

Copyright © 2009 Jian Liu and Yanbin Sang. 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

By using the fixed-point index theorem, we consider the existence of positive solutions for the following nonlinear higher-order four-point singular boundary value problem on time scales uΔn(t)+g(t)f(u(t),uΔ(t),…,uΔn−2(t))=0, 0<t<T; uΔi(0)=0, 0≤i≤n−3; αuΔn−2(0)−βuΔn−1(ξ)=0, n≥3; γuΔn−2(T)+δuΔn−1(η)=0, n≥3, where α>0, β≥0, γ>0, δ≥0, ξ, η∈(0,T), ξ<η, and g:(0,T)→[0,+∞) is rd-continuous.