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