Open AccessStability of some differential equations of the fourth-order and fifth-order
Author(s) -
B. S. Kalitine
Publication year - 2019
Publication title -
žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika/žurnal belorusskogo gosudarstvennogo universiteta. matematika, informatika
Language(s) - English
Resource type - Journals
eISSN - 2617-3956
pISSN - 2520-6508
DOI - 10.33581/2520-6508-2019-1-18-27
Subject(s) - mathematics , lyapunov function , nonlinear system , differential equation , mathematical analysis , ordinary differential equation , scalar (mathematics) , order (exchange) , constant coefficients , stability (learning theory) , linear differential equation , physics , computer science , geometry , quantum mechanics , finance , machine learning , economics
The article is devoted to the study of the problem of stability of nonlinear ordinary differential equations by the method of semi-definite Lyapunov’s functions. The types of fourth-order and fifth-order scalar nonlinear differential equations of general form are singled out, for which the sign-constant auxiliary functions are defined. Sufficient conditions for stability in the large are obtained for such equations. The results coincide with the necessary and sufficient conditions in the corresponding linear case. Studies emphasize the advantages in using the semi-positive functions in comparison with the classical method of applying Lyapunov’s definite positive functions.