International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 767-774

On the existence of a periodic solution of a nonlinear ordinary differential equation

Hsin Chu1 and Sunhong Ding2

1University of Marylnd, College Park 20742, MD, USA
2Institute of Mathematical Sciences, Academia Sinica, Chendu, China

Received 8 March 1996; Revised 10 December 1996

Copyright © 1998 Hsin Chu and Sunhong Ding. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Consider a planar forced system of the following form {dxdt=μ(x,y)+h(t)dydt=ν(x,y)+g(t), where h(t) and g(t) are 2π-periodic continuous functions, t(,) and μ(x,y) and ν(x,y) are continuous and satisfy local Lipschitz conditions. In this paper, by using the Poincáre's operator we show that if we assume the condltions, (C1), (C2) and (C3) (see Section 2), then there is at least one 2π-periodic solution. In conclusion, we provide an explicit example which is not in any class of known results.