Geodesic
Stability of solutions and the problem of Aizerman for sixth-order differential equations
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2020), pp. 49-58

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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. 
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     author = {B. S. Kalitin},
     title = {Stability of solutions and the problem of {Aizerman} for sixth-order differential equations},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {49--58},
     publisher = {mathdoc},
     volume = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2020_2_a3/}
}
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B. S. Kalitin. Stability of solutions and the problem of Aizerman for sixth-order differential equations. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2020), pp. 49-58. http://geodesic.mathdoc.fr/item/BGUMI_2020_2_a3/