Boundary Value Problems
Volume 2008 (2008), Article ID 457028, 12 pages
Research Article

Positive Solutions of Singular Initial-Boundary Value Problems to Second-Order Functional Differential Equations

Fengfei Jin and Baoqiang Yan

School of Mathematics Sciences, Shandong Normal University, Jinan 250014, China

Received 23 August 2007; Revised 9 January 2008; Accepted 5 August 2008

Academic Editor: Raul Manasevich

Copyright © 2008 Fengfei Jin and Baoqiang Yan. 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.


Positive solutions to the singular initial-boundary value problems x=f(t,xt),0<t<1,x0=0,x(1)=0, are obtained by applying the Schauder fixed-point theorem, where xt(u)=x(t+u)(0t1) on [r,0] and f(,):(0,1)×(C+\{0})R+(C+={xC([r,0],R),x(t)0,t[r,0]}) may be singular at φ(u)=0(ru0) and t=0. As an application, an example is given to demonstrate our result.