Electron. J. Diff. Eqns., Vol. 2008(2008), No. 159, pp. 1-10.

Multiple positive solutions of fourth-order four-point boundary-value problems with changing sign coefficient

Zheng Fang, Chunhong Li, Chuanzhi Bai

Abstract:
In this paper, we investigate the existence of multiple positive solutions of the fourth-order four-point boundary-value problems
$$\displaylines{ y^{(4)}(t) = h(t) g(y(t), y''(t)), \quad 0 < t < 1, \cr y(0) = y(1) = 0, \cr a y''(\xi_1)-b y'''(\xi_1) = 0, \quad c y''(\xi_2)+d y'''(\xi_2) = 0, }$$
where $0 < \xi_1 < \xi_2 < 1$. We show the existence of three positive solutions by applying the Avery and Peterson fixed point theorem in a cone, here $h(t)$ may change sign on $[0, 1]$.

Submitted September 3, 2008. Published December 3, 2008.
Math Subject Classifications: 34B10, 34B15.
Key Words: Four-point boundary-value problem; positive solution; fixed point on a cone.

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  Zheng Fang
School of Science, Jiangnan University
Wuxi, Jiangsu 214122, China
email: fangzhengm@yahoo.com.cn
Chunhong Li
Department of Mathematics, Huaiyin Teachers College
Huaian, Jiangsi 223300, China
email: lichshy2006@126.com
Chuanzhi Bai
Department of Mathematics, Huaiyin Teachers College
Huaian, Jiangsi 223300, China
email: czbai8@sohu.com

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