Geodesic
Lyapunov Functions, Krasnosel'skii Canonical Domains, and the Existence of Poisson Bounded Solutions
Matematičeskie zametki, Tome 108 (2020) no. 5, pp. 750-756 Cet article a éte moissonné depuis la source Math-Net.Ru

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The notions of Poisson boundedness and Poisson partial boundedness of solutions of systems are introduced. Based on the Lyapunov function method and Krasnosel'skii's method of canonical domains, a sufficient condition for the existence of Poisson bounded solutions is obtained.
Keywords: Poisson bounded solution, partially bounded solution, Lyapunov function, Krasnosel'skii canonical domain.
Mots-clés : existence of solutions 
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K. S. Lapin. Lyapunov Functions, Krasnosel'skii Canonical Domains, and the Existence of Poisson Bounded Solutions. Matematičeskie zametki, Tome 108 (2020) no. 5, pp. 750-756. http://geodesic.mathdoc.fr/item/MZM_2020_108_5_a8/

[1] T. Yoshizawa, “Liapunovs function and boundedness of solutions”, Funkcialaj Ekvacioj, 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 | Zbl

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

[5] 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

[6] V. I. Vorotnikov, “Ob ustoichivosti i ustoichivosti po chasti peremennykh chastichnykh polozhenii ravnovesiya nelineinykh dinamicheskikh sistem”, Dokl. AN, 389:3 (2003), 332–337 | MR

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

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

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

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

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

[13] K. S. Lapin, “Vektor-funktsii Lyapunova i ogranichennost v predele po Puassonu reshenii sistem differentsialnykh uravnenii”, Matem. zametki, 104:1 (2018), 74–86 | DOI | Zbl

[14] K. S. Lapin, “Totalnaya ogranichennost po Puassonu reshenii sistem differentsialnykh uravnenii i vektor-funktsii Lyapunova”, Matem. zametki, 104:2 (2018), 243–254 | DOI | Zbl

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

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