Abstract and Applied Analysis
Volume 2010 (2010), Article ID 261741, 19 pages
doi:10.1155/2010/261741
Research Article

Multiple Positive Solutions of a Second Order Nonlinear Semipositone m-Point Boundary Value Problem on Time Scales

Chengjun Yuan1,2 and Yongming Liu1

1Department of Mathematics, East China Normal University, Shanghai 200241, China
2School of Mathematics and Computer, Harbin University, Harbin, Heilongjiang 150086, China

Received 28 April 2010; Revised 26 June 2010; Accepted 7 September 2010

Academic Editor: Allan C Peterson

Copyright © 2010 Chengjun Yuan and Yongming Liu. 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

In this paper, we study a general second-order m-point boundary value problem for nonlinear singular dynamic equation on time scales uΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+λq(t)f(t,u(t))=0, t∈(0,1)𝕋, u(ρ(0))=0, u(σ(1))=∑i=1m-2αiu(ηi). This paper shows the existence of multiple positive solutions if f is semipositone and superlinear. The arguments are based upon fixed-point theorems in a cone.