Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 115, pp. 1-7.
Title: Double solutions of three-point boundary-value problems for
second-order differential equations
Author: Johnny Henderson (Baylor Univ., Waco, Texas, USA)
Abstract:
A double fixed point theorem is applied to yield the
existence of at least two nonnegative solutions for the three-point
boundary-value problem for a second-order differential equation,
$$\displaylines{
y'' + f(y)=0,\quad 0 \leq t \leq 1,\cr
y(0) =0,\quad y(p) - y(1) = 0,
}$$
where $0 < p < 1$ is fixed, and $f:\mathbb{R} \to [0, \infty)$ is
continuous.
Submitted September 16, 2003. Published October 5, 2004.
Math Subject Classifications: 34B15, 34B10, 34B18.
Key Words: Fixed point theorem; three-point; boundary-value problem.