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.