PERIODIC SOLUTIONS OF DISSIPATIVE FUNCTIONAL DIFFERENTIAL EQUATIONS

Abstract

We consider periodic, finite delay differential equations. The first two theorems prove dissipativeness for these equations generalizing a result of Pliss. We use dissipativeness to prove the existence of a periodic solution by a result of Hale and Lopes. In our special case we give short, elementary proof for their theorem. We also present a theorem using Liapunov functionals to show dissipativeness.