Boundary Value Problems
Volume 2010 (2010), Article ID 254928, 16 pages
Research Article

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

Department of Mathematics, Beihua University, JiLin City 132013, China

Received 25 November 2009; Accepted 10 March 2010

Academic Editor: Ivan T. Kiguradze

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.


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 m3, 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.