Existence of solutions for some nonautonomous partial functional differential equations with state-dependent delay (Q777463)

The aim of this paper is to prove the existence of mild solutions for some non-autonomous partial functional differential equations where the delay depends on the solutions. The linear part is not necessarily densely defined and it satisfies Oka and Tanaka's property. The nonlinear part satisfies the Carathéodory conditons and not necessarily Lischitzian. The authors used the compactness procedure to prove the existence of the mild solutions. For that goal, the authors assumed that the evolution family generated by the linear part is compact and they used the Leary-Schauder alternative. An axample is provided for some reaction-diffusion equation with stated dependent delay.