Electron. J. Diff. Eqns., Vol. 2007(2007), No. 16, pp. 1-8.

Positive solutions for semipositone fourth-order two-point boundary value problems

Dandan Yang, Hongbo Zhu, Chuanzhi Bai

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

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Dandan Yang
Department of Mathematics, Yanbian University
Yanji, Jilin 133000, China.
Department of Mathematics, Huaiyin Teachers College
Huaian, Jiangsu 223001, China
email: yangdandan2600@sina.com
Hongbo Zhu
Department of Mathematics, Yanbian University
Yanji, Jilin 133000, China.
Department of Mathematics, Huaiyin Teachers College
Huaian, Jiangsu 223001, China
email: zhuhongbo8151@sina.com
Chuanzhi Bai
Department of Mathematics
Huaiyin Teachers College
Huaian, Jiangsu 223001, China
email: czbai8@sohu.com

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