Korepanova K. Asymptotic representations of solutions of differential equations with regularly varying nonlinearities

The dissertation is devoted to the research of asymptotic behavior of solutions of essentially nonlinear non-autonomous ordinary differential equations of n-th order. The necessary and sufficient existence conditions of solutions, some derivative of which tends to a nonzero constant, as an argument tends to infinity, have been obtained. Using the introduced class of solutions, for each of the possible values of the parameter we got the asymptotic representations of solutions and their derivatives of order up to n-1 inclusive. The question on the quantity of solutions with found representations has been also solved.