Periodic solutions of linear second order differential equations with deviating argument

Abstract

This paper is concerned with the question of the existence of periodic solutions of periodic linear second order differential equations with deviating argument. Using a fixed point theorem for multivalued mappings and results concerning boundary value problems for such equations, we prove that the existence of periodic solutions of both types of differential inequalities implies the existence of periodic solutions. This result, in turn, is used to obtain the existence of periodic solutions of certain nonlinear differential equations with deviating argument.