Existence of solutions in the alpha-norm for partial functional differential equations with infinite delay

Abstract

In this work, we prove a result on the local existence of mild solution in the $\alpha$-norm for some partial functional differential equations with infinite delay. We suppose that the linear part generates a compact analytic semigroup. The nonlinear part is just assumed to be continuous. We use the compactness method, to show the main result of this work. Some application is provided