Betsko I. Investigation of the structure of the set of continuous solutions of difference equations systems

The dissertation is devoted to the study of issues of the existence of continuous solutions of systems of difference equations and the study of their properties. A method of constructing a whole family of continuous bounded solutions for wide classes of homogeneous systems of difference equations with linear deviation of an argument is developed. For systems of inhomogeneous difference equations, the conditions of existence of continuous bounded solutions are established and the structure of their set in a hyperbolic case is investigated. The researches were extended to systems of nonlinear functional difference equations, in particular, the conditions for existence of continuous bounded solutions of such systems were established, the structure of the set of continuous bounded solutions in a hyperbolic case was investigated. This paper also establishes the conditions for existence of bounded over the entire real axis nonlinear functional-difference equations and investigates their properties.