Vladova O. Asymptotic representation for solutions of cyclic sufficiently nonlinear systems of differential equations

The dissertation represents a study of a cyclic sufficiently nonlinear system of differential equations with nonlinearities represented by normalized properly varying functions. For this system of equations, a new class of solutions is introduced. For this class of solutions, the methodology of research is worked out. The methodology differs depending on the value of the parameters of solutions. Using different methodologies for different values of parameters, the necessary and sufficient conditions for the existence of the introduced class of solutions are derived. Moreover, for different values of parameters, the asymptotic formulas for that solutions are obtained (when argument aims to a special point). In case of certain conditions, closed-form asymptotic representations are found.