Anti-Lyapunov method for systems of discrete equations Original Research Article

In the present paper problems concerning the qualitative behaviour of solutions of discrete equations are considered. A general principle which gives a guarantee that the graph of at least one solution stays in a prescribed domain is formulated. As a consequence, the auxiliary tool—namely, a method of regular polyfacial sets—is developed and an application of the general principle is given. This application is based, with exceptions, on the fact that points of the boundary of a domain considered are strict egress points. Such a situation is often (in the theory of ordinary differential equations) termed the Anti-Lyapunov case. Illustrative applications and examples are given and open problems are formulated.