Boundary Value Problems 
Volume 2008 (2008), Article ID 457028, 12 pages
doi:10.1155/2008/457028
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

Recommended by Raul Manasevich

Abstract

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) (0≤t≤1) on [−r,0] and f(⋅,⋅):(0,1)×(C+\{0})→R+(C+={x∈C([−r,0],R), x(t)≥0, ∀t∈[−r,0]}) may be singular at φ(u)=0 (−r≤u≤0) and t=0. As an application, an example is given to demonstrate our result.