Periodic solutions for a class of ordinary differential equations

Abstract

A T-periodic solution to the differential equation x + c x ′ + g ( x ) = f ( t ) ≡ f ( t + T ) x + cx’ + g(x) = f(t) \equiv f(t + T) is shown to exist whenever a simple condition on g holds, provided c ≠ 0 c \ne 0 . No assumption is made concerning the growth of g. The condition on g is necessary if g is either an increasing or a decreasing function.