We establish sufficient conditions for the existence of periodic R-solutions of linear differential inclusions with impulses at fixed times.
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A. I. Panasyuk and V. V. Panasyuk, Asymptotic Optimization of Nonlinear Control Systems [in Russian], Belorussian University, Minsk (1977).
A. A. Tolstonogov, Differential Inclusions in a Banach Space [in Russian], Nauka, Novosibirsk (1986).
R. J. Aumann, “Integrals of set-valued functions,” J. Math. Anal. Appl., 12, No. 1, 1–12 (1965).
A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).
V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore (1989).
L. Erbe and W. Krawcewicz, “Existence of solutions to boundary value problems for impulsive second order differential inclusions,” Rocky Mt. J. Math., 22, No. 2, 519–539 (1992).
P. J. Watson, “Impulsive differential inclusions,” Nonlin. World, 4, No. 4, 395–402 (1997).
N. V. Plotnikova, “Periodic solutions of linear impulsive differential inclusions,” Nelin. Kolyvannya, 7, No. 4, 495–515 (2004).
V. I. Blagodatskikh and A. F. Filippov, “Differential inclusions and optimal control,” Tr. Mat. Inst. Akad. Nauk SSSR, 169, 194–252 (1985).
V. P. Demidovich, Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).
A. A. Lyapunov, “On completely additive vector functions,” Izv. Akad. Nauk SSSR, Ser. Mat., No. 6, 465–478 (1940).
C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities. Applications to Free Boundary Problems, Wiley, New York (1984).
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 9, pp. 1287–1296, September, 2008.
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Skripnik, N.V. Periodic solutions of linear impulsive differential inclusions. Ukr Math J 60, 1498–1508 (2008). https://doi.org/10.1007/s11253-009-0136-x
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DOI: https://doi.org/10.1007/s11253-009-0136-x