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
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
and are -periodic continuous functions, and
are continuous and satisfy local Lipschitz conditions. In this
paper, by using the Poincáre's operator we show that if we assume the condltions,
(see Section 2), then there is at least one -periodic
solution. In conclusion, we provide an explicit example which is not in any class
of known results.