Copyright © 2010 Xuezhe Lv and Minghe Pei. 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

The existence and uniqueness of positive solution is obtained for the singular second-order m-point boundary value problem u′′(t)+f(t,u(t))=0 for t∈(0,1), u(0)=0, u(1)=∑i=1m-2αiu(ηi), where m≥3, αi>0 (i=1,2,…,m-2), 0<η1<η2<⋯<ηm-2<1 are constants, and f(t,u) can have singularities for t=0 and/or t=1 and for u=0. The main tool is the perturbation technique and Schauder fixed point theorem.