Necessary and sufficient conditions for the regularity and stability of solutions for some partial neutral functional differential equations with infinite delay

In this paper we give necessary and sufficient conditions for the regularity and stability of solutions for some partial neutral functional differential equations with infinite delay. We establish also a generalization and extension of the characterization of the infinitesimal generator of the solution semigroup. To illustrate our abstract results, we study the stability of the neutral Lotka–Volterra model with diffusion.