Vector Lyapunov Functions and Ultimate Poisson Boundedness of Solutions of Systems of Differential Equations
Matematičeskie zametki, Tome 104 (2018) no. 1, pp. 74-86

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Various forms of uniform-ultimate Poisson boundedness of solutions and of ultimate Poisson equiboundedness of solutions are introduced. Sufficient conditions for various forms of uniform-ultimate Poisson boundedness and of ultimate Poisson equiboundedness of solutions are obtained by using the method of vector Lyapunov functions.
Keywords: boundedness of solutions, Poisson boundedness of solutions, vector Lyapunov function, partial boundedness of solutions, partially controlled initial conditions.
K. S. Lapin. Vector Lyapunov Functions and Ultimate Poisson Boundedness of Solutions of Systems of Differential Equations. Matematičeskie zametki, Tome 104 (2018) no. 1, pp. 74-86. http://geodesic.mathdoc.fr/item/MZM_2018_104_1_a7/
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[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. S. 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. S. 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. S. 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. M. Matrosov, Metod vektornykh funktsii Lyapunova: analiz dinamicheskikh svoistv nelineinykh sistem, Fizmatlit, M., 2000 | Zbl

[7] K. S. Lapin, “Vektor-funktsii Lyapunova i chastichnaya ogranichennost reshenii s chastichno kontroliruemymi nachalnymi usloviyami”, Differents. uravneniya, 52:5 (2016), 572–578 | DOI | MR | Zbl

[8] K. S. Lapin, “Chastichnaya totalnaya ogranichennost reshenii sistem differentsialnykh uravnenii s chastichno kontroliruemymi nachalnymi usloviyami”, Matem. zametki, 99:2 (2016), 239–247 | DOI | MR | Zbl

[9] V. I. Vorotnikov, Yu. G. Martyshenko, “K teorii chastichnoi ustoichivosti nelineinykh dinamicheskikh sistem”, Izv. RAN. Teoriya i sistemy upravleniya, 2010, no. 5, 23–31 | MR | Zbl

[10] 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

[11] 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

[12] V. V. Nemytskii, V. V. Stepanov, Kachestvennaya teoriya differentsialnykh uravnenii, Gostekhizdat, M., 1947 | MR | Zbl