Periodic solutions for some partial neutral functional differential equations

Abstract

In this work, we study the existence of periodic solutions for partial neutral functional differential equation. We assume that the linear part is not necessarily densely defined and satisfies the Hille-Yosida condition. In the nonhomogeneous linear case, we prove that the existence of a bounded solution on ℝ⁺ implies the existence of a periodic solution. In nonlinear case, we use the concept of boundedness and ultimate boundedness to prove the existence of periodic solutions.