Boundary Value Problems
Volume 2007 (2007), Article ID 79090, 14 pages
doi:10.1155/2007/79090

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

Abstract

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=1m−2αiu(ηi), where 0<η1<η2<⋯<ηm−2≤1/2, αi>0 for i=1,2,…,m−2 with ∑i=1m−2αi<1,m≥3. 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.