On a Class of Impulsive Functional-Differential Equations with Nonatomic Difference Operator

We establish conditions for the existence and uniqueness of the solutions of nonlinear functional-differential equations with impulsive action in a Banach space. The equation under consideration is not solved for the derivative. It is assumed that the characteristic operator pencil corresponding to the linear part of the equation satisfies a constraint of parabolic type in the right half-plane. Applications to partial functional-differential equations not of Kovalevskaya type are considered.