Geodesic
Krasnosel'skii canonical domains and the existence of non-negative Poisson bounded solutions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2022), pp. 10-17.

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On the basis of the vector Lyapunov functions method and the Krasnoselskii method of canonical domains, a sufficient condition for the existence of non-negative Poisson bounded solutions is obtained. In addition, a sufficient condition for the existence of partially non-negative partially Poisson bounded solutions is obtained.
Keywords: vector Lyapunov function, Krasnosel'skii canonical domain, Poisson boundedness of solution, partial Poisson boundedness of solution, non-negativity of solution. 
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K. S. Lapin. Krasnosel'skii canonical domains and the existence of non-negative Poisson bounded solutions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2022), pp. 10-17. http://geodesic.mathdoc.fr/item/IVM_2022_7_a1/

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

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

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

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

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

[6] Krasnoselskii M. A., Polozhitelnye resheniya operatornykh uravnenii, Fizmatlit, M., 1962 | MR

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

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

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

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