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

Abstract

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.