Bounded solutions of a system of linear inhomogeneous differential equations of the first order with rectangular matrices

  • A. A. Boichuk Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv
  • M. A. Elishevich National University of Building and Architecture, Kyiv https://orcid.org/0000-0003-2933-6379

Abstract

UDC 517.926.7

Conditions for existence are determined and bounded solutions of a system of linear inhomogeneous differential equations of the first order with rectangular matrices are constructed.

References

A. M. Samojlenko, M. I. Shkil`, V. P. Yakovecz`, Лiнiйнi системи диференцiальних рiвнянь з виродженнями (Ukrainian) [[Linijni sistemi diferenczial`nikh rivnyan` z virodzhennyami]], Vishha shk., Kiyiv (2000).

M. A. Elishevich, Некоторые свойства жордановых наборов векторов матрицы относительно оператора, содержащего дифференцирование (Russian) [[Nekotory`e svojstva zhordanovy`kh naborov vektorov matriczy` otnositel`no operatora, soderzhashhego differenczirovanie , Zhurn. obchislyuv. ta prikl. matematiki, No 2 (108), 119 – 134 (2012).

M. A. Elishevich, Задача Коши для системы линейных неоднородных дифференциальных уравнений первого порядка с прямоугольными матрицами (Russian) [[Zadacha Koshi dlya sistemy` linejny`kh neodnorodny`kh differenczial`ny`kh uravnenij pervogo poryadka s pryamougol`ny`mi matriczami, Nelinijni kolivannya]], Нелiнiйнi коливання, 16, No 2, 173 – 190 (2013).

A. A. Boichuk, A. M. Samoilenko, Generalized inverse operators and Fredholm boundary-value problems, 2nd ed., Translated from the Russian by Peter V. Malyshev. Inverse and Ill-posed Problems Series, 59. De Gruyter, Berlin, 2016. xvi+296 pp. ISBN: 978-3-11-037839-9; 978-3-11-037844-3; 978-3-11-038735-3 https://doi.org/10.1515/9783110378443

Kreĭn, S. G. Линейные уравнения в банаховом пространстве (Russian) [[Linear equations in a Banach space]] Izdat. ``Nauka'', Moscow, 1971. 104 pp.

V. A. Trenogin, Функциональный анализ. (Russian) [[<>emFunctional analysis]] ``Nauka'', Moscow, 1980. 496 pp.

V. F. Chistyakov, A. A. Shcheglova, Избранные главы теории алгебро-дифференциальных систем. (Russian) [[Selected chapters in the theory of algebro-differential systems]] ``Nauka'', Novosibirsk, 2003. 320 pp. ISBN: 5-02-031730-6

Yu. L. Daletskiĭ, M. G. Kreĭn, Устойчивость решений дифференциальных уравнений в банаховом пространстве. (Russian) [[Stability of solutions of differential equations in Banach space]] Nonlinear Analysis and its Applications Series. Izdat. ``Nauka'', Moscow, 1970. 534 pp.

Y. Sibuya, Some global properties of matrixes of functions of one variable, Math. Anal., 161, No 1, 67 – 77 (1965) https://doi.org/10.1007/BF01363248

W. Wasow, On holomorphically similar matrices J, Math. Anal. and Appl., No 4, 202 – 206 (1962) https://doi.org/10.1016/0022-247X(62)90050-1

Published
17.06.2020
How to Cite
BoichukA. A., and ElishevichM. A. “Bounded Solutions of a System of Linear Inhomogeneous Differential Equations of the First Order With Rectangular Matrices”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, no. 6, June 2020, pp. 758-75, doi:10.37863/umzh.v72i6.1059.
Section
Research articles