On the recurrent solutions of a class of non-linear differential equations

Abstract

1. This paper is concerned with certain properties of the solutions of differential equations of the typewhere f, g have continuous partial derivatives up to the second order satisfying Lipschitz conditions in some bounded domain and are periodic in t with period 2π, ω is a positive constant and k is a small parameter. If f = 0, (1·1) is equivalent toan equation representing the forced vibrations of a quasi-linear system of one degree of freedom.