Abstract
We present sufficient conditions for the asymptotic equivalence of a nonlinear impulsive system and a nonlinear system without pulses. We also consider the case of the asymptotic equivalence of a weakly nonlinear impulsive system and a linear system with pulses.
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A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).
V. P. Demidovich, Lectures on Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).
F. Brauer, “Nonlinear differential equations with forcing terms,” Proc. Amer. Math. Soc., 15, No. 5, 758–765 (1964).
L. Nirenberg, Topics in Nonlinear Functional Analysis [Russian translation], Mir, Moscow (1977).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 4, pp. 514–521, April, 2007.
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Stanzhyts’kyi, O.M., Misyats’, O.O. Asymptotic equivalence of impulsive systems. Ukr Math J 59, 577–587 (2007). https://doi.org/10.1007/s11253-007-0037-9
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DOI: https://doi.org/10.1007/s11253-007-0037-9