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

Hsin Chu and Sunhong Ding

International Journal of Mathematics and Mathematical Sciences, 1998, vol. 21, 1-8

Abstract:

Consider a planar forced system of the following form { d x d t = μ ( x , y ) + h ( t ) d y d t = − ν ( x , y ) + g ( t ) , where h ( t ) and g ( t ) are 2 π -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, ( C 1 ) , ( C 2 ) and ( C 3 ) (see Section 2), then there is at least one 2 π -periodic solution. In conclusion, we provide an explicit example which is not in any class of known results.

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:527812

DOI: 10.1155/S0161171298001070

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