Geodesic
Ultimate Boundedness in the Sense of Poisson of Solutions~to~Systems~of~Differential Equations and Lyapunov Functions
Matematičeskie zametki, Tome 103 (2018) no. 2, pp. 223-235.

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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.
Keywords: boundedness of solutions, boundedness of solutions in the sense of Poisson, Lyapunov function, partial boundedness of solutions, partially controllable initial conditions. 
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     author = {K. S. Lapin},
     title = {Ultimate {Boundedness} in the {Sense} of {Poisson} of {Solutions~to~Systems~of~Differential} {Equations} and {Lyapunov} {Functions}},
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K. S. Lapin. Ultimate Boundedness in the Sense of Poisson of Solutions~to~Systems~of~Differential Equations and Lyapunov Functions. Matematičeskie zametki, Tome 103 (2018) no. 2, pp. 223-235. http://geodesic.mathdoc.fr/item/MZM_2018_103_2_a5/

[1] T. Yoshizawa, “Liapunov's function and boundedness of solutions”, Funkcial. Ekvac., 2 (1959), 95–142 | MR | Zbl

[2] V. V. Rumyantsev, A. S. Oziraner, Ustoichivost i stabilizatsiya dvizheniya otnositelno chasti peremennykh, Nauka, M., 1987 | MR | Zbl

[3] K. C. Lapin, “Ogranichennost v predele reshenii sistem differentsialnykh uravnenii po chasti peremennykh s chastichno kontroliruemymi nachalnymi usloviyami”, Differents. uravneniya, 49:10 (2013), 1281–1286 | MR | Zbl

[4] K. C. Lapin, “Chastichnaya ravnomernaya ogranichennost reshenii sistem differentsialnykh uravnenii s chastichno kontroliruemymi nachalnymi usloviyami”, Differents. uravneniya, 50:3 (2014), 309–316 | DOI | MR | Zbl

[5] K. C. Lapin, “Ravnomernaya ogranichennost reshenii sistem differentsialnykh uravnenii po chasti peremennykh s chastichno kontroliruemymi nachalnymi usloviyami”, Matem. zametki, 96:3 (2014), 393–404 | DOI | Zbl

[6] V. I. Vorotnikov, Yu. G. Martyshenko, “K teorii chastichnoi ustoichivosti nelineinykh dinamicheskikh sistem”, Izv. RAN. Teor. i sist. upravl., 2010, no. 5, 23–31 | MR | Zbl

[7] V. I. Vorotnikov, Yu. G. Martyshenko, “K zadacham chastichnoi ustoichivosti dlya sistem s posledeistviem”, Tr. IMM UrO RAN, 19, no. 1, 2013, 49–58 | MR

[8] V. I. Vorotnikov, Yu. G. Martyshenko, “Ob ustoichivosti po chasti peremennykh “chastichnykh” polozhenii ravnovesiya sistem s posledeistviem”, Matem. zametki, 96:4 (2014), 496–503 | DOI | MR | Zbl

[9] V. V. Nemytskii, V. V. Stepanov, Kachestvennaya teoriya differentsialnykh uravnenii, URSS, M., 2004 | MR | Zbl