Boundary Value Problems
Volume 2007 (2007), Article ID 79090, 14 pages
Research Article

Existence of Symmetric Positive Solutions for an m-Point Boundary Value Problem

Yongping Sun and Xiaoping Zhang

Department of Electron and Information, Zhejiang University of Media and Communications, Hangzhou 310018, Zhejiang, China

Received 23 June 2006; Revised 17 December 2006; Accepted 11 March 2007

Academic Editor: Colin Rogers

Copyright © 2007 Yongping Sun and Xiaoping Zhang. 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.


We study the second-order m-point boundary value problem u''(t)+a(t)f(t,u(t))= 0, 0<t<1, u(0)=u(1)=i=1m2αiu(ηi), where 0<η1<η2<<ηm21/2, αi>0 for i=1,2,,m2 with i=1m2αi<1,m3. a:(0,1)[0,) is continuous, symmetric on the interval (0,1), and maybe singular at t=0 and t=1, f:[0,1]×[0,)[0,) is continuous, and f(,x) is symmetric on the interval [0,1] for all x[0,) and satisfies some appropriate growth conditions. By using Krasnoselskii's fixed point theorem in a cone, we get some existence results of symmetric positive solutions.