Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 16, pp. 1-8.
Title: Positive solutions for semipositone fourth-order
two-point boundary value problems
Authors: Dandan Yang (Yanbian Univ., Yanji, China)
Hongbo Zhu (Yanbian Univ., Yanji, China)
Chuanzhi Bai (Huaiyin Teachers College, china)
Abstract:
In this paper we investigate the existence of positive solutions of
the following nonlinear semipositone fourth-order two-point
boundary-value problem with second derivative:
$$\displaylines{
u^{(4)}(t) = f(t, u(t), u''(t)), \quad 0 \leq t \leq 1, \cr
u'(1) = u''(1) = u'''(1) = 0, \quad k u(0) = u'''(0),
}$$
where $-6 < k < 0$, $f \geq - M$, and $M$ is a positive constant.
Our approach relies on the Krasnosel'skii fixed point theorem.
Submitted August 3, 2006. Published January 23, 2007.
Math Subject Classifications: 34B16.
Key Words: Boundary value problem; Positive solution;
semipositone; fixed point