Positive Solutions to Boundary-Value Problem of Fourth-Order Nonlinear Functional Differential Equation

Journal of South China University of Technology (Natural Science Edition) ›› 2006, Vol. 34 ›› Issue (7): 129-132.

• Mathematical Sciences • Previous Articles

Positive Solutions to Boundary-Value Problem of Fourth-Order Nonlinear Functional Differential Equation

Song Chang-xiu Weng Pei-xuan

School of Mathematical Sciences,South China Normal Univ.,Guangzhou 510631,Guangdong,China

Received:2005-09-02 Online:2006-07-25 Published:2006-07-25
Contact: 宋常修(1975-)，男，在职博士生，广东工业大学讲师，主要从事泛函微分方程的研究． E-mail:scx168@sohu.com
About author:宋常修(1975-)，男，在职博士生，广东工业大学讲师，主要从事泛函微分方程的研究．
Supported by:
国家自然科学基金资助项目(10571064)；广东省自然科学基金资助项目(011471)

Abstract

Abstract:

This paper deals with the boundary-value problems of a class of fourth-order nonlinear functi0hal differen-tial equation. By transforming the boundary-value problem into the corresponding fixed-point problem of a complete-ly continuous operator,the sufficient condition for the existence of the positive solutions to the problem is given via the fixed-point theorem in cones and the inequality evaluation technology. Thus,the existing results of the boun-dary-value problem for the corresponding ordinary differential equation are extended. The applicability of the ob-tained results is finally proved by examples.

Key words: singularity, nonlinearity, functional differential equation, positive solution, cone

Song Chang-xiu Weng Pei-xuan. Positive Solutions to Boundary-Value Problem of Fourth-Order Nonlinear Functional Differential Equation[J]. Journal of South China University of Technology (Natural Science Edition), 2006, 34(7): 129-132.

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Positive Solutions to Boundary-Value Problem of Fourth-Order Nonlinear Functional Differential Equation

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