PERIODIC-SOLUTIONS OF DISSIPATIVE FUNCTIONAL-DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

We consider periodic, infinite delay differential equations. We invest igate dissipativeness for these equations. Massat proved that dissipat ive, periodic, infinite delay equations have a periodic solution. For our purpose we need a weaker dissipativeness, so we prove Massat's the orem from this weak dissipativeness in an elementary way. Then we exte nd a theorem of Pliss giving a necessary and sufficient condition for this weak dissipativeness. We also present a theorem using Liapunov fu nctionals to show the weak dissipativeness and hence the existence of a periodic solution.