Vitrychenko I. Critical cases of stability by Liapunov of nonautonomous nonlinear differential systems

Objects of the research are nonperiodic nonlinear differential systems. The aim of the research is an obtaining on a new sufficient conditions in algebraic critical cases. For attainment of the aim there was constructed a method of the research based on application of a generalized "cutoff", "frozen" transformations, O. Perron principle of a stability (quasilinear systems) and combination of O. Kostin methtod of research of regular solutions of higher orders, method of Liapunov functions and lemma on stability into annular domain containing the position of equilibrium (essentially nonlinear systems). Results were extended on equations of higher orders and applied to some problems of a stability theory.