Geodesic
Hayers–Ulam–Rassias stability of linear systems of differential equations with generalized action and delay
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2024), pp. 71-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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For linear systems of differential equations with delay subject to generalized influence, a formalization of the concept of Highers–Ulam–Rassias stability is proposed. The cases are considered when the system has a single reaction to a generalized impact and when the system's reaction is not unique. Sufficient conditions for such stability are established for the systems of differential equations under consideration.
Keywords: Hyers–Ulam–Rassias stability, generalized action, delay, linear system. 
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     author = {A. N. Sesekin and A. D. Kandrina and N. V. Gredasova},
     title = {Hayers{\textendash}Ulam{\textendash}Rassias stability of linear systems of differential equations with generalized action and delay},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {71--84},
     year = {2024},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2024_12_a6/}
}
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A. N. Sesekin; A. D. Kandrina; N. V. Gredasova. Hayers–Ulam–Rassias stability of linear systems of differential equations with generalized action and delay. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2024), pp. 71-84. http://geodesic.mathdoc.fr/item/IVM_2024_12_a6/

[1] Ulam S., Nereshennye matematicheskie zadachi, Nauka, M., 1964

[2] Hyers D.H., “On the Stability of the Linear Functional Equation”, Proc. Nat. Acad. Sci., 27:4 (1941), 222–224 | DOI | MR | Zbl

[3] Alsina C., Ger R., “On some Inequalities and Stability Results Related to the Exponential Function”, J. Inequal. Appl., 2:4 (1998), 373–380 | MR | Zbl

[4] Rassias Th.M., “On the stability of the linear mapping in Banach spaces”, Proc. Amer. Math. Soc., 72:2 (1978), 297–300 | DOI | MR | Zbl

[5] Rus I.A., “Ulam stability of ordinary differential equations”, Studia Uinv. “BABES-BOLYAI”, Math., LIV:4 (2009), 125–133 | MR | Zbl

[6] Rus I.A., “Remarks on Ulam stability of the operatorial equations”, Fixed Point Theory, 10:2 (2009), 305–320 | MR | Zbl

[7] Arutyunov A.V., “Zadacha o tochkakh sovpadeniya mnogoznachnykh otobrazhenii i ustoichivost po Ulamu–Khaiersu”, Dokl. Akad. nauk, 455:4 (2014), 379–383 | DOI | Zbl

[8] Zada A., Pervaiz B., Alzabut J., Shah S.O., “Further results on Ulam stability for a system of first-order nonsingular delay differential equations”, Demonstratio Math., 53:1 (2020), 225–235 | DOI | MR | Zbl

[9] Zavalishchin S.T., Sesekin A.N., Dynamic Impulse Systems: Theory and Applications, Kluwer Academic Publ., Dolrbrecht, 1997 | MR | Zbl

[10] Sesekin A.N., Fetisova Yu.V., “Funktsionalno-differentsialnye uravneniya v prostranstve funktsii ogranichennoi variatsii”, Tr. in-ta Matem. i mekhan. UrO RAN, 15, no. 4, 2009, 226–233

[11] Zainullina E.Z., Pavlenko V.S., Sesekin A.N., Gredasova N.V., “Ob ustoichivosti po Ulamu–Khaiersu reshenii differentsialnykh uravnenii pervogo poryadka s obobschennym vozdeistviem”, Mater. Voronezh. mezhd. vesennei matem. shkoly «Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXXII» Voronezh, 3–9 maya 2021 g. Ch. 2, Itogi nauki i tekhn. Sovrem. matem. i ee pril. Temat. obz., 209, VINITI RAN, M., 2022, 25–32 | DOI | MR

[12] Pavlenko V., Sesekin A., “Ulam–Hyers Stability of First and Second Order DifferentiałEquations with Discontinuous Trajectories”, $16$th Int. Conf. on Stability and Oscillations of Nonlinear Control Systems, Pyatnitskiy's Conf., STAB 2022, ed. V.N. Tkhai, IEEE Xplore, 2022

[13] Sesekin A.N., Kandrina A.D., “Hyers–Ulam–Rassias stability of nonlinear differential equations with a generalized actions on the right-hand side”, Ural Math. J., 9:1 (2023), 147–152 | DOI | MR | Zbl

[14] Gredasova N.V., Pavlenko V., Sesekin A.N., Shulyaeva K.S., “Ob ustoichivosti po Khaiersu–Ulamu–Rassiasu lineinykh differentsialnykh uravnenii s obobschennym vozdeistviem v pravoi chasti i s zapazdyvaniem”, Mater. VIII mezhd. konf. «Matematika, ee prilozheniya i matematicheskoe obrazovanie», MPMO'23, Izd-vo VSGUTU, Ulan-Ude, 2023, 72–74

[15] Samoilenko A.M., Perestyuk N.A., Differentsialnye uravneniya s impulsnym vozdeistviem, Vischa shk., Kiev, 1987

[16] Wang G., Zhou M., Sun L., “Hyers-Ulam stability of linear differential equations of first order”, Appl. Math. Let., 21:10 (2008), 1024–1028 | DOI | MR | Zbl

[17] Lukoyanov N.Yu., Funktsionalnye uravneniya Gamiltona–Yakobi i zadachi upravleniya s nasledstvennoi informatsiei, UrFU, Ekaterinburg, 2011