Abstract
The notions of different types of boundedness in the sense of Poisson of solutions to systems of differential equations are introduced. Sufficient conditions are obtained for different types of boundedness of solutions in the sense of Poisson, which are introduced in the paper.
Similar content being viewed by others
References
T. Yoshizawa, “Liapunov’s function and boundedness of solutions,” Funkcial. Ekvac. 2, 95–142 (1959).
V. V. Rumyantsev and A. S. Oziraner, Stability and Stabilization of Motion with Respect to a Part of the Variables (Nauka, Moscow, 1987) [in Russian].
K. C. Lapin, “Ultimate boundedness with respect to part of the variables of solutions of systems of differential equations with partly controllable initial conditions,” Differ. Uravn. 49 (10), 1281–1286 (2013) [Differ. Equations 49 (10), 1246–1251 (2013)].
K. C. Lapin, “Partial uniform boundedness of solutions of systems of differential equations with partly controlled initial conditions,” Differ. Uravn. 50 (3), 309–316 (2014) [Differ. Equations 50 (3), 305–311 (2014)].
K. C. Lapin, “Uniform boundedness in part of the variables of solutions to systems of differential equations with partially controllable initial conditions,” Mat. Zametki 96 (3), 393–404 (2014) [Math. Notes 96 (3–4), 369–378 (2014)].
V. I. Vorotnikov and Yu. G. Martyshenko, “On partial stability theory of nonlinear dynamic systems,” Izv. Ross. Akad. Nauk, Teor. Sist. Upravl. No. 5, 23–31 (2010) [J. Comput. Syst. Sci. 49 (5), 702–709 (2010)].
V. I. Vorotnikov and Yu. G. Martyshenko, “On problems of partial stability for systems with aftereffect,” in Tr. Inst. Mat. Mekh. (Ural Branch Russian Academy of Sciences) (2013), Vol. 19, No. 1 pp. 49–58, [in Russian].
V. I. Vorotnikov and Yu. G. Martyshenko, “Stability in part of variables of “partial” equilibria of systems with aftereffect,” Mat. Zametki 96 (4), 496–503 (2014) [Math. Notes 96 (3–4), 477–483 (2014)].
V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations (URSS, Moscow, 2004) [in Russian].
Author information
Authors and Affiliations
Additional information
Original Russian Text © K. S. Lapin, 2018, published in Matematicheskie Zametki, 2018, Vol. 103, No. 2, pp. 223–235.
Rights and permissions
About this article
Cite this article
Lapin, K.S. Ultimate Boundedness in the Sense of Poisson of Solutions to Systems of Differential Equations and Lyapunov Functions. Math Notes 103, 221–231 (2018). https://doi.org/10.1134/S0001434618010236
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0001434618010236