Differential equations and Optimal control

Stability of solutions and the problem of Aizerman for sixth-order differential equations

B. S. Kalitin

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

Abstract: This article is devoted to the investigation of stability of equilibrium of ordinary differential equations using the method of semi-definite Lyapunov’s functions. Types of scalar nonlinear sixth-order differential equations for which regular constant auxiliary functions are used are emphasized. Sufficient conditions of global asymptotic stability and instability of the zero solution have been obtained and it has been established that the Aizerman problem has a positive solution concerning the roots of the corresponding linear differential equation. Studies highlight the advantages of using semi-definite functions compared to definitely positive Lyapunov's functions.

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

UDC: 517.925

Received: 09.06.2020

DOI: 10.33581/2520-6508-2020-2-49-58