Electron. J. Diff. Eqns., Vol. 2006(2006), No. 68, pp. 1-11.

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

Chuanzhi Bai, Qing Yang, Jing Ge

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.

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Chuanzhi Bai
Department of Mathematics, Huaiyin Teachers College
Huaian, Jiangsi 223001, China;
and Department of Mathematics, Nanjing University
Nanjing 210093, China
email: czbai8@sohu.com
Qing Yang
Department of Mathematics, Huaiyin Teachers College
Huaian, Jiangsi 223001, China
email: yangqing3511115@163.com
Jing Ge
Department of Mathematics, Huaiyin Teachers College
Huaian, Jiangsi 223001, China
email: gejing0512@163.com

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