Advances in Difference Equations
Volume 2010 (2010), Article ID 620459, 10 pages
doi:10.1155/2010/620459
Research Article

Monotone Iterative Technique for First-Order Nonlinear Periodic Boundary Value Problems on Time Scales

Ya-Hong Zhao and Jian-Ping Sun

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

Received 12 February 2010; Revised 17 May 2010; Accepted 26 June 2010

Academic Editor: Paul Eloe

Copyright © 2010 Ya-Hong Zhao and 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.

Abstract

We investigate the following nonlinear first-order periodic boundary value problem on time scales: xΔ(t)+p(t)x(σ(t))=f(t,x(t)), t∈[0,T]T, x(0)=x(σ(T)). Some new existence criteria of positive solutions are established by using the monotone iterative technique.