The stability of solutions of certain operator equations with lagging arguments
Izvestiya. Mathematics, Tome 1 (1967) no. 2, pp. 381-390
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We consider the equation \begin{gather*} y(t_1,\dots,t_n)-\sum_{q_1\dots q_n}A_{q_1\dots q_n}y(t_1-m^{(1)}_{q_1\dots q_n}a_1,\dots,t_n-m^{(n)}_{q_1\dots q_n}a_n)=f \\ (m^{(k)}_{q_1\dots q_n} \text{ -- are integers} \geqslant0;\ a_k>0;\ 0\leqslant t_1,\dots,t_n\infty), \end{gather*} where the $A_{q_1\dots q_n}=A_{q_1\dots q_n}(t_1,\dots,t_n)$ are continuous linear operator-functions operating in a complex Banach space. We establish necessary and sufficient tests for the boundedness of the solutions $y(t_1,\dots,t_n)$ of these equations for all bounded right-hand sides $f=f(t_1,\dots,t_n)$
@article{IM2_1967_1_2_a10,
author = {Z. I. Rekhlitskii},
title = {The stability of solutions of certain operator equations with lagging arguments},
journal = {Izvestiya. Mathematics},
pages = {381--390},
year = {1967},
volume = {1},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a10/}
}
Z. I. Rekhlitskii. The stability of solutions of certain operator equations with lagging arguments. Izvestiya. Mathematics, Tome 1 (1967) no. 2, pp. 381-390. http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a10/
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