On a differential game in an abstract parabolic system

We consider the game problem of approach for a system whose dynamics is described by a differential operator equation in a Hilbert space. The equation is written in an implicit form with generally non-invertible operator multiplying 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 a right half-plane. Using the method of resolving functionals, we obtain sufficient conditions for the approach of a dynamical vector of the system to a cylindrical terminal set. Applications to systems described by partial differential equations are considered.