This article is cited in 1 paper

Differential equations and Optimal control

Stability of some differential equations of the fourth-order and fifth-order

B. S. Kalitin

Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

Abstract: 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.

Keywords: scalar differential equation; equilibrium; stability; semi-definite Lyapunov’s function.

UDC: 517.925

DOI: 10.33581/2520-6508-2019-1-18-27