On stability of a class of discrete systems

The problem of stability properties for the solutions of nonlinear difference equations is considered. The approach used is to study the behavior of the solutions of nonlinear difference equations with respect to solutions of a nonlinear difference equation. This is a more general setting than the comparison principle in which the comparison equation is a linear difference equation.The principal technique employed is an extension of Liapunov's direct method. A series of theorems is obtained yielding criteria for the behavior of solutions in terms of existence of the Liapunov-type function with appropriate properties.