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.