Yeromina T. Continuous solutions of systems of difference-functional equations and their properties.

In the dissertation work investigated the structure of the continuous solution set of systems of difference-functional equations with linear deflections of an argument and studied their properties. Developed the method of building a whole family of continuous bounded for (T - some quite large positive constant) solutions for broad classes of homogeneous systems of linear difference-functional equations. For systems of heterogeneous linear difference-functional equations determined existence conditions of continuous bounded for solutions and investigated the structure of their set in critical and hyperbolic cases. The research is extended on systems of difference equations with many argument deflections, in particular proved the theorem of unity of a continuous bounded for solution. Nevertheless conditions are given on which it has infinitely many continuous for solutions. Obtained a generalization for systems of non-linear functional equations, being investigated issues of existence and unity of continuous bounded for solutions of such equations and being studied their properties.