ℬ𝒞-total stability and almost periodicity for some partial functional differential equations with infinite delay

Abstract

In this paper, we study the existence of an almost periodic solution for some partial functional differential equation with infinite delay. We assume that the linear part is nondensely defined and satisfies the known Hille-Yosida condition. We prove if the null solution of the homogeneous equation is ℬ𝒞-total stable, then the nonhomogeneous equation has an almost periodic solution.