Differential Games in a Banach Space without Discrimination.

The paper is a continuation of author's research on the existence of an ε-equilibrium in the sense of piecewise program strategies in two-person zero-sum games associated with a nonlinear nonautonomous controlled differential equation in a Banach space and a general cost functional. As in the preceding paper on this subject, the main result consists in sufficient conditions for an ε-equilibrium. The difference is that this time we investigate a game without discriminating the players or fixing a Volterra chain. The results are illustrated as applied to a game associated with a nonlinear pseudoparabolic partial differential equation governing the evolution of an electric field in a semiconductor. [ABSTRACT FROM AUTHOR]