Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 159, pp. 1-10.
Title: Multiple positive solutions of fourth-order four-point
boundary-value problems with changing sign coefficient
Authors: Zheng Fang (Jiangnan Univ., Wuxi, China)
Chunhong Li (Huaiyin Teachers College, Jiangsi, China)
Chuanzhi Bai (Huaiyin Teachers College, Jiangsi, China)
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 03, 2008.
Math Subject Classifications: 34B10, 34B15
Key Words: Four-point boundary-value problem; positive solution;
fixed point on a cone.