Mild solutions for some nonautonomous partial functional differential equations with infinite delay

Abstract

The aim of this work is to establish several results on the existence of mild solutionse nondensely nonautonomous partial functional differential equations with infinite delay in Banach spaces. We assume that the linear part is not necessarily densely defined and generates an evolution family. We show the local existence of the mild solutions which may blow up at the finite time. Secondly, we get the existence of global mild solutions. For illustration, we propose applications for distributed delay and discrete delay.