Periodic solutions for partial neutral non densely differential equations

Abstract

This work investigates the existence of periodic solutions for the following partial neutral nonautonomous functional differential equation (1) where the linear operator A is not necessarily densely defined and satisfies the Hille–Yosida condition, , , is a family of bounded linear operators from into X and the nonlinear delayed part F satisfies some locally Lipschitz conditions. More precisely, we study the Massera problem for the existence of a τ-periodic solution of (1). Then, we prove for , in the dichotomic case, the existence, uniqueness and conditional stability of the periodic solution. Finally, our results are illustrated by an application.