Differentiability of Semi-Flow for Impulsive Evolution Equation with State-Dependent Delay

In this paper, we study the impulsive evolution equation with state-dependent delay by the theory of operator semigroup in Banach spaces. Under conditions that both nonlinearity and impulsive functions are Lipschitz continuous, we obtain the existence and uniqueness results of mild solution. Furthermore, we prove the differentiability of a semi-flow defined by a continuously differentiable solution operator under the appropriate condition.