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In this paper, we prove the existence of mild solutions for a first order impulsive neutral evolution differential inclusion with state-dependent delay. We transform it into an integral equation and use a fixed point theorem for condensing multi-valued maps. As an application of the main theorem, we consider the case when the multi-valued nonlinearity has… (More)

In this paper we prove some existence and uniqueness results for pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to a class of partial functional differential equation in Banach spaces. The main technique is based upon some appropriate composition theorems combined with the Banach contraction mapping principle and fractional… (More)

In this paper, we are focused upon the global uniqueness results for a stochastic integro-differential equation in Fréchet spaces. The main results are proved by using the resolvent operators combined with a nonlinear alternative of Leray-Schauder type in Fréchet spaces due to Frigon and Granas. As an application, a controllability result with one parameter… (More)