Boundary Value Problems
Volume 2010 (2010), Article ID 254928, 16 pages
doi:10.1155/2010/254928

Existence and Uniqueness of Positive Solution for a Singular Nonlinear Second-Order m-Point Boundary Value Problem

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.