Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 127, pp. 1-7.

Title: Eigenvalues and symmetric positive solutions for a
       three-point boundary-value problem
       
Author: Yongping Sun (Hangzhou Radio & TV Univ., China)

Abstract: 
 In this paper, we consider the
 second-order three-point boundary-value problem
 $$\displaylines{
 u''(t)+f(t,u,u',u'')=0,\quad  0\leq t\leq 1,\cr
 u(0)=u(1)=\alpha u(\eta).
 }$$
 Under suitable conditions and using Schauder fixed point
 theorem, we prove the existence of at least one symmetric positive
 solution. We also study the existence of positive
 eigenvalues for this problem. We emphasis the
 highest-order derivative occurs nonlinearly in our problem.
 
Submitted September 15, 2005. Published November 23, 2005.
Math Subject Classifications: 34B10, 34B15.
Key Words: Symmetric positive solution; 
           three-point boundary-value problem; 
           Schauder fixed point theorem; eigenvalue.