Electron. J. Diff. Eqns., Vol. 2006(2006), No. 41, pp. 1-10.

Positive solutions for a functional delay second-order three-point boundary-value problem

Chuanzhi Bai, Xinya Xu

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
$$\displaylines{ - x''(t) = f(t, x(t), x(t - \tau), x_t), \quad 0 less than t less than 1, \cr x_0 = \phi, \quad x(1) = x(\eta), }$$
where $\phi \in C[- \tau, 0]$, $0 less than \tau less than 1/4$, and $\tau less than \eta less than 1$.

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.

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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
  Xinya Xu
Department of Mathematics, Huaiyin Teachers College
Huaian, Jiangsi 223001, China
email: xinyaxu@hytc.edu.cn

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