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Izv. Akad. Nauk SSSR Ser. Mat., 1967, Volume 31, Issue 2, Pages 391–400 (Mi izv2545)  

This article is cited in 1 scientific paper (total in 1 paper)

The stability of solutions of certain operator equations with lagging arguments

Z. I. Rekhlitskii


Abstract: We consider the equation
\begin{gather*} y(t_1,…,t_n)-\sum_{q_1…q_n}A_{q_1…q_n}y(t_1-m^{(1)}_{q_1…q_n}a_1,…,t_n-m^{(n)}_{q_1…q_n}a_n)=f
(m^{(k)}_{q_1…q_n} – are integers \geqslant0; a_k>0; 0\leqslant t_1,…,t_n<\infty), \end{gather*}
where the $A_{q_1…q_n}=A_{q_1…q_n}(t_1,…,t_n)$ are continuous linear operator-functions operating in a complex Banach space. We establish necessary and sufficient tests for the boundedness of the solutions $y(t_1,…,t_n)$ of these equations for all bounded right-hand sides $f=f(t_1,…,t_n)$

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English version:
Mathematics of the USSR-Izvestiya, 1967, 1:2, 381–390

Bibliographic databases:

UDC: 517.9
MSC: 47A50, 46E15, 41A58
Received: 04.07.1966

Citation: Z. I. Rekhlitskii, “The stability of solutions of certain operator equations with lagging arguments”, Izv. Akad. Nauk SSSR Ser. Mat., 31:2 (1967), 391–400; Math. USSR-Izv., 1:2 (1967), 381–390

Citation in format AMSBIB
\Bibitem{Rek67}
\by Z.~I.~Rekhlitskii
\paper The stability of solutions of certain operator equations with lagging arguments
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1967
\vol 31
\issue 2
\pages 391--400
\mathnet{http://mi.mathnet.ru/izv2545}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=213929}
\zmath{https://zbmath.org/?q=an:0166.12403}
\transl
\jour Math. USSR-Izv.
\yr 1967
\vol 1
\issue 2
\pages 381--390
\crossref{https://doi.org/10.1070/IM1967v001n02ABEH000563}


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  • http://mi.mathnet.ru/eng/izv/v31/i2/p391

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Z. I. Rekhlitskii, “Stability tests for the solutions of linear operator equations with discrete and continuous lags in the arguments”, Math. USSR-Izv., 4:2 (1970), 465–477  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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