Periodicity and stability of solutions to neutral differential equations with $\varphi $-Lipschitz and infinite delays

We prove the existence and uniqueness of a periodic solution to neutral function partial differential equations with infinite delay of the form $$ \frac {\partial Fu_t}{\partial t}= A(t)Fu_t +g(t,u_t)\quad \mbox {for } t \gt 0,\quad u(t)=\phi (t)\quad \hb