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 non-autonomous 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 $A(\cdot)$ is assumed to be non-densely defined and verified by the Acquistapace-Terreni conditions. Finally, we propose an application to illustrate our results.