On the existence of mild solutions of some partial functional integrodifferential equations with non continuous state-dependent delay function (Q6657896)

The aim of this paper is to prove the existenceof a mild solution for some partial functional integrodifferential equations with state-dependent delay. The fact that the delay dependson the state presents bih challenge and serious problem. We have severalproblems thatcan be modeled by state-dependent delay.Here, we try to solve even if the delay depends on the state. The main working tools are based on resolvent operators, Banach's fixed point, Schauder's fixed point theorems and the concept of regulated functions.For Banach's fixed point theorem, we assume that coefficients are Lipshitzian. In order to apply Schauder's fixed point theorem, we need more additional conditions, forexample the resolvent operator must be compact. The paper presents new contributions in the fields.