Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 14, pp. 1-14.

Title: Positive solutions to  generalized second-order three-point
       integral boundary-value problems

Authors: Saowaluk Chasreechai (King Mongkut's Univ., Bangkok, Thailand)
         Jessada Tariboon     (King Mongkut's Univ., Bangkok, Thailand)
	 
Abstract:
 In this article, by using Krasnoselskii's fixed point theorem,
 we obtain single and multiple positive solutions to the
 nonlinear second-order three-point integral boundary value
 problem
 $$\displaylines{ 
 u''(t)+a(t)f(u(t))=0,\quad 0<t<T, \cr
 u(0)=\beta\int_0^{\eta}u(s)ds,\quad
 \alpha\int_0^{\eta}u(s)ds=u(T),
 }$$
 where $0<\eta<T$, $0<\alpha<\frac{2T}{\eta^2}$,
 $0<\beta<\frac{2T-\alpha\eta^2}{\eta(2T-\eta)}$ are given constants.
 As an application, we give some examples that illustrate our results.

Submitted October 22, 2010. Published January 26, 2011.
Math Subject Classifications: 34B15, 34K10.
Key Words: Positive solution; three-point boundary value problem; 
           fixed point theorem; cone.