Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 68, pp. 1-11.

Title: Existence of positive solutions for  boundary-value 
       problems for singular higher-order functional 
       differential equations

Authors: Chuanzhi Bai (Huaiyin Teachers College, China)
         Qing Yang  (Huaiyin Teachers College, China)
	 Jing Ge  (Huaiyin Teachers College, China)

Abstract: 
 We study  the existence of positive  solutions  for the
 boundary-value problem of the singular higher-order functional
 differential equation
 $$\displaylines{
 (L y^{(n-2)})(t)+h(t)f(t, y_t)=0, \quad  \hbox{for } t\in [0, 1],\cr
 y^{(i)}(0) = 0, \quad  0 \leq i \leq n - 3, \cr
 \alpha y^{(n-2)}(t)-\beta  y^{(n-1)} (t)=\eta (t),
 \quad  \hbox{for } t \in [- \tau, 0],\cr
 \gamma y^{(n-2)}(t) + \delta  y^{(n-1)}(t) = \xi (t),
 \quad \hbox{for } t \in [1, 1 + a],
 }$$
 where $ Ly := -(p y')' + q y$, $p \in C([0, 1],(0, + \infty))$,
 and  $q \in C([0, 1], [0, + \infty))$. Our main tool is the fixed
 point theorem on a cone.
 
Submitted April 21, 2006. Published July 6, 2006.
Math Subject Classifications: 34K10, 34B16.
Key Words: Boundary value problem;  higher-order;
    positive solution; functional differential equation; 
    fixed point.