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.