On the stability of third order differential equations

  • Boris S. Kalitine Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

Abstract

In this paper, we study the problem of stability of the equilibrium of nonlinear ordinary differential equations by the method of semi-definite Lyapunov’s functions. We have identified nonlinear third order differential equations of general form for which the choice of a semi-definite function does not present difficulties. For such equations, sufficient conditions of stability and asymptotic stability (local and global) are obtained. The results of asymptotic stability of the equilibrium coincide with necessary and sufficient conditions in the corresponding linear case. Consequently, they meet generally accepted requirements. The conducted studies show that the use of semi-defined positive functions can give advantages in comparison with the classical method of application of Lyapunov’s definite positive functions.

Author Biography

Boris S. Kalitine, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

PhD (physics and mathematics); professor at the department of analytical economics and econometrics, faculty of economy

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Published
2019-01-19
Keywords: differential equation, equilibrium, stability, semi-definite Lyapunov's function
How to Cite
Kalitine, B. S. (2019). On the stability of third order differential equations. Journal of the Belarusian State University. Mathematics and Informatics, 2, 25-33. Retrieved from https://journals.bsu.by/index.php/mathematics/article/view/781
Issue
No 2 (2018): Journal of the Belarusian State University. Mathematics and Informatics
Section
Differential Equations and Optimal Control

Copyright (c) 2018 Journal of the Belarusian State University. Mathematics and Informatics

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