Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 65798, 8 pages
doi:10.1155/DDNS/2006/65798

Existence of positive solutions of PBVPs for first-order difference equations

Yinggao Zhou

School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, China

Received 5 January 2006; Accepted 13 March 2006

Copyright © 2006 Yinggao Zhou. 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 consider the existence of positive solutions for the following first-order periodic boundary value problem: x(n+1)=x(n)−f(n,x(n)), 0≤n≤ω−1, x(0)=x(ω). Some criteria for existence of positive solutions of the above difference boundary problem are established by using Krasnosel'skiĭ's fixed point theorem, and some multiplicity results of positive solutions are also derived.