Periodic Solutions of a Class of Neutral Nonautonomous Partial Differential Equations in Fading Memory Spaces

The present work deals with the existence and periodicity of solutions to nonautonomous partial differential equations of retarded, infinite, and neutral type in the framework of fading memory space, which is defined axiomatically. In our strategy, we rely on Sadovskii’s fixed-point theorem. On the other hand, the family of linear operators A( · ) is assumed to be nondensely defined and verified by the Acquistapace–Terreni conditions. Finally, we propose an application to illustrate our results.