Advances in Difference Equations
Volume 2010 (2010), Article ID 235296, 14 pages
Research Article

Existence of Positive Solutions for Semipositone Higher-Order BVPS on Time Scales

Department of Mathematics, Beihua University, JiLin City 132013, China

Received 4 December 2009; Revised 16 March 2010; Accepted 29 March 2010

Academic Editor: Alberto Cabada

Copyright © 2010 Yuguo Lin and Minghe Pei. 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 offer conditions on semipositone function f(t,u0,u1,,un-2) such that the boundary value problem, uΔn(t)+f(t,u(σn-1(t)),uΔ(σn-2(t)),,uΔn-2(σ(t)))=0, t(0,1)𝕋, n2, uΔi(0)=0, i=0,1,,n-3, αuΔn-2(0)-βuΔn-1(0)=0, γuΔn-2(σ(1))+δuΔn-1(σ(1))=0, has at least one positive solution, where 𝕋 is a time scale and f(t,u0,u1,,un-2)C([0,1]×[0,)n-1,(-,)) is continuous with f(t,u0,u1,,un-2)-M for some positive constant M.