Sv-asymptotically T-periodic solutions for some class of neutral differential equations — Model of the heat equation

In this paper, we aim to present the concept of [Formula: see text]-asymptotically T-periodic functions taking values in a Banach space and investigate some of their properties. Also, we establish conditions under which semi linear evolution equations in a Banach space have a unique global mild [Formula: see text]-asymptotically T-periodic solution. Then, we apply the results obtained to prove the existence and uniqueness of [Formula: see text]-asymptotically [Formula: see text]-periodic mild solutions to a nonautonomous semi linear differential equations.