We establish necessary and sufficient conditions for the stability of one class of impulsive linear differential equations with delay.
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A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).
M. O. Perestyuk and O. S. Chernikova, “Some modern aspects of the theory of impulsive differential equations,” Ukr. Mat. Zh., 60, No. 1, 81–94 (2008).
A. A. Boichuk, N. A. Perestyuk, and A. M. Samoilenko, “Periodic solutions of impulsive differential systems in critical cases,” Differents. Uravn., 27, No. 9, 1516–1521 (1991).
A. A. Martynyuk, J. H. Shen, and I. P. Stavroulakis, “Stability theorems in impulsive functional differential equations with infinite delay,” in: A. A. Martynyuk (editor), Advances in Stability Theory at the End of the 20th Century, Taylor & Francis, London (2003), pp. 153–174.
V. I. Slyn’ko, “On conditions for the stability of motion of linear impulsive systems with delay,” Prikl. Mekh., 41, No. 6, 130–138 (2005).
M. O. Perestyuk and V. Yu. Slyusarchuk, “Conditions for the existence of nonoscillating solutions of nonlinear differential equations with delay and pulse influence in a Banach space,” Ukr. Mat. Zh., 55, No. 6, 790–798 (2003).
V. Lakshmikantham, S. Leela, and A. A. Martynyuk, Stability of Motion: The Comparison Method [in Russian], Naukova Dumka, Kiev (1991).
É. Goursat, Cours d’Analyse Mathématique [Russian translation], Vol. 1, Part 2, Gostekhteorizdat, Moscow (1934).
E. Jahnke, F. Emde, and F. Lösch, Tables of Higher Functions, McGraw-Hill, New York (1960).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 9, pp. 1200–1207, September, 2009.
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Ivanov, I.L., Slyn’ko, B.I. Conditions for the stability of an impulsive linear equation with pure delay. Ukr Math J 61, 1417–1427 (2009). https://doi.org/10.1007/s11253-010-0286-x
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DOI: https://doi.org/10.1007/s11253-010-0286-x