Geodesic
Guiding functional families, Lyapunov vector functions, and the existence of Poisson bounded solutions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2021), pp. 31-39.

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

On the basis of the method of guiding functional families and the method of Lyapunov vector functions we obtain sufficient condition for the existence of Poisson bounded solutions, as well as a sufficient condition for the existence of partially Poisson bounded solutions of systems of differential equations.
Keywords: vector Lyapunov function, rotation of the vector field, guiding function, guiding function, guiding functional family, Poisson boundedness of solution, partial Poisson boundedness of solution. 
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     title = {Guiding functional families, {Lyapunov} vector functions, and the existence of {Poisson} bounded solutions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
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}
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K. S. Lapin. Guiding functional families, Lyapunov vector functions, and the existence of Poisson bounded solutions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2021), pp. 31-39. http://geodesic.mathdoc.fr/item/IVM_2021_9_a3/

[1] Matrosov V.M., Metod vektornykh funktsii Lyapunova: analiz dinamicheskikh svoistv nelineinykh sistem, Fizmatlit, M., 2001

[2] Lyapunov A.M., Obschaya zadacha ob ustoichivosti dvizheniya, Izdanie Kharkovsk. matem. o-va, Kharkov, 1892

[3] Krasnoselskii M.A., Operator sdviga po traektoriyam differentsialnykh uravnenii, Nauka, M., 1966

[4] Zvyagin V.G., Kornev S.V., Metod napravlyayuschikh funktsii i ego modifikatsii, LENAND, M., 2018

[5] Lapin K.S., “Ravnomernaya ogranichennost po Puassonu reshenii sistem differentsialnykh uravnenii i vektor-funktsii Lyapunova”, Differents. uravneniya, 54:1 (2018), 40–50 | Zbl

[6] Lapin K.S., “Ogranichennost v predele po Puassonu reshenii sistem differentsialnykh uravnenii i funktsii Lyapunova”, Matem. zametki, 103:2 (2018), 223–235 | Zbl

[7] Lapin K.S., “Vysshie proizvodnye funktsii Lyapunova i ogranichennost v predele po Puassonu reshenii sistem differentsialnykh uravnenii”, Sib. matem. zhurn., 59:6 (2018), 1383–1388 | Zbl

[8] Yoshizawa T., “Liapunovs function and boundedness of solutions”, Funkcial. Ekvac., 2 (1959), 95–142 | Zbl

[9] Rumyantsev V. V., Oziraner A. S., Ustoichivost i stabilizatsiya dvizheniya po otnosheniyu k chasti peremennykh, Nauka, M., 1987

[10] Dold A., Lektsii po algebraicheskoi topologii, Mir, M., 1976

[11] Kartashev A. P., Rozhdestvenskii B. L., Obyknovennye differentsialnye uravneniya i osnovy variatsionnogo ischisleniya, Nauka, M., 1980