Boundary Value Problems
Volume 2009 (2009), Article ID 685040, 6 pages
Research Article

Existence of Positive Solution to Second-Order Three-Point BVPs on Time Scales

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received 19 April 2009; Accepted 14 September 2009

Academic Editor: Kanishka Perera

Copyright © 2009 Jian-Ping Sun. 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 are concerned with the following nonlinear second-order three-point boundary value problem on time scales xΔΔ(t)=f(t,x(t)), t[a,b]𝕋, x(a)=0, x(σ2(b))=δx(η), where a,b𝕋 with a<b,    η(a,b)𝕋 and 0<δ<(σ2(b)a)/(ηa). A new representation of Green's function for the corresponding linear boundary value problem is obtained and some existence criteria of at least one positive solution for the above nonlinear boundary value problem are established by using the iterative method.