Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 41, pp. 1-10.

Title: Positive solutions for a functional delay
       second-order  three-point boundary-value problem
       
Authors: Chuanzhi Bai (Huaiyin Teachers College, China)
         Xinya Xu (Huaiyin Teachers College, China)

Abstract: 
 We establish criteria for the existence of positive solutions to
 the three-point boundary-value problems expressed by
 second-order functional delay differential  equations of the form
 $$\displaylines{
 - x''(t) = f(t, x(t), x(t - \tau), x_t), \quad 0 <t< 1, \cr
 x_0 = \phi, \quad x(1) = x(\eta),
 }$$
 where $\phi \in C[- \tau, 0]$,  $0 < \tau < 1/4$, and
 $\tau < \eta < 1$.
  
Submitted August 10, 2005. Published March 26, 2006.
Math Subject Classifications: 34K10, 34B10.
Key Words: Functional delay differential equation; 
           boundary value problem; positive solutions; 
	   fixed point index.