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.

Abstract

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, n≥2, 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]×ℝ[0,∞)n-1,ℝ(-∞,∞)) is continuous with f(t,u0,u1,…,un-2)≥-M for some positive constant M.