Electron. J. Diff. Eqns., Vol. 2004(2004), No. 115, pp. 1-7.

Double solutions of three-point boundary-value problems for second-order differential equations

Johnny Henderson

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 $0$ less than $p$ less than $1$ 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.

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Johnny Henderson
Department of Mathematics
Baylor University
Waco, TX 76798-7328, USA
email: Johnny_Henderson@baylor.edu

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