Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

A relationship between the periodic and the Dirichlet BVPs of singular differential equations*

Meirong Zhanga1

a1 Department of Applied Mathematics, Tsinghua University, Beijing 100084, People's Republic of China; Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, Georgia 30332, U.S.A., e-mail: mzhang@math.tsinghua.edu.cn

Abstract

In this paper, a relationship between the periodic and the Dirichlet boundary value problems for second-order ordinary differential equations with singularities is established. This relationship may be useful in explaining the difference between the nonresonance of singular and nonsingular differential equations. Using this relationship, we give in this paper an existence result of positive periodic solutions to singular differential equations when the singular forces satisfy some strong force condition at the singularity 0 and some linear growth condition at infinity.

(Received June 20 1997)

(Revised October 29 1997)

Footnotes

* Project supported by the National Natural Science Foundation of China and the Tsinghua University Education Foundation.