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

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
@article{MZM_2018_104_1_a7,
     author = {K. S. Lapin},
     title = {Vector {Lyapunov} {Functions} and {Ultimate} {Poisson} {Boundedness} of {Solutions} of {Systems} of {Differential} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {74--86},
     publisher = {mathdoc},
     volume = {104},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_1_a7/}
}
TY  - JOUR
AU  - K. S. Lapin
TI  - Vector Lyapunov Functions and Ultimate Poisson Boundedness of Solutions of Systems of Differential Equations
JO  - Matematičeskie zametki
PY  - 2018
SP  - 74
EP  - 86
VL  - 104
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_104_1_a7/
LA  - ru
ID  - MZM_2018_104_1_a7
ER  - 
%0 Journal Article
%A K. S. Lapin
%T Vector Lyapunov Functions and Ultimate Poisson Boundedness of Solutions of Systems of Differential Equations
%J Matematičeskie zametki
%D 2018
%P 74-86
%V 104
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_104_1_a7/
%G ru
%F MZM_2018_104_1_a7
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/

[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