Geodesic
Stability of some differential equations of the fourth-order and fifth-order
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2019), pp. 18-27.

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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. 
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B. S. Kalitin. Stability of some differential equations of the fourth-order and fifth-order. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2019), pp. 18-27. http://geodesic.mathdoc.fr/item/BGUMI_2019_1_a2/

[1] A. I. Ogurtsov, “Ob ustoichivosti v tselom reshenii nelineinykh differentsialnykh uravnenii tretego i chetvertogo poryadkov”, Izvestiya vuzov. Matematika, 1(2) (1958), 124-129 | MR | Zbl

[2] A. I. Ogurtsov, “Ob ustoichivosti reshenii dvukh nelineinykh differentsialnykh uravnenii tretego i chetvertogo poryadkov”, Prikladnaya matematika i mekhanika, 23(1) (1959), 179–181 | MR | Zbl

[3] A. I. Ogurtsov, “Ob ustoichivosti reshenii nekotorykh nelineinykh differentsialnykh uravnenii tretego i chetvertogo poryadkov”, Izvestiya vuzov. Matematika, 3 (1959), 200–209 | MR

[4] E. A. Barbashin, “Funktsii Lyapunova”, Moskva: Nauka, 1970, 240 | MR | Zbl

[5] A. I. Ogurtsov, “Ob ustoichivosti reshenii nekotorykh nelineinykh differentsialnykh uravnenii pyatogo i shestogo poryadkov”, Matematicheskie zapiski, 3(2) (1962), 78-93

[6] A. M. Lyapunov, “Obschaya zadacha ob ustoichivosti dvizheniya”, Moskva: Gostekhizdat, 1950, 472 | MR

[7] B. S. Kalitin, “Ustoichivost differentsialnykh uravnenii (Metod znakopostoyannykh funktsii Lyapunova)”, Saarbryukken: LAP, 2012, 223

[8] B. S. Kalitin, “Ob ustoichivosti uravneniya Lenara”, Izvestiya vuzov. Matematika, 10 (2018), 17-28 | Zbl

[9] B. S. Kalitin, “Ob ustoichivosti differentsialnykh uravnenii tretego poryadka”, Zhurnal Belorusskogo gosudarstvennogo universiteta. Matematika. Informatika, 2 (2018), 25–33 | Zbl

[10] N. Rush, P. Abets, M. Lalua, “Pryamoi metod Lyapunova v teorii ustoichivosti”, Moskva: Mir, 1980, 300 | MR

[11] B. S. Kalitin, “Ustoichivost dinamicheskikh sistem (Metod znakopostoyannykh funktsii Lyapunova)”, Saarbryukken: LAP, 2013, 259

[12] V. V. Amelkin, “Differentsialnye uravneniya”, Minsk: BGU, 2012, 288

[13] B. P. Demidovich, “Lektsii po matematicheskoi teorii ustoichivosti”, Moskva: Nauka, 1967, 472 | MR | Zbl