Abstract
The conditions are established, under which periodic solutions of pulse evolutionary systems with unbounded (inx) operators on the right-hand sides exist and are stable.
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Yu. A. Mitropol'skii, A. M. Samoilenko, and N. A. Perestyuk, “Averaging method in systems with pulse effects,”Ukr. Mat. Zh.,37, No. 1, 56–64 (1985).
A. M. Samoilenko and N. A. Perestyuk,Differential Equations with Pulse Effects [in Russian], Vyshcha Shkola, Kiev (1987).
Yu. V. Rogovchenko and S. I. Trofimchuk,Periodic Solutions of Weakly Nonlinear Parabolic Partial Differential Equations and Their Stability [in Russian], Preprint 86.65, Institute of Mathematics, Ukrainian Academy of Science, Kiev (1986).
Yu. V. Rogovchenko and S. I. Trofimchuk, “Bounded and periodic solutions of weakly nonlinear pulse evolutionary systems,”Ukr. Mat. Zh.,39, No. 2, 260–264 (1987).
Yu. V. Rogovchenko, “On the uniqueness of a periodic solution of a nonlinear pulse evolutionary system,” in:Differential Equations -with Parameter [in Russian], Institute of Mathematics, Ukrainian Academy of Science, Kiev (1989), pp. 94–98.
A. M. Samoilenko, N. A. Perestyuk, and S. I. Trofimchuk,The Problem of “Beating” in Pulse Systems [in Russian], Preprint 90.11, Institute of Mathematics, Ukrainian Academy of Science, Kiev (1990).
D. Henry,Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag-Berlin-Heidelberg, New York (1981).
M. A. Krasnosel'skii, P. P. Zabreiko, E. I. Pustyl'nik, and P. E. Sobolevskii,Integral Operators in the Spaces of Summable Functions [in Russian], Nauka, Moscow (1966).
M. Miclavcic, “Stability for semilinear equations with noninvertible linear operator,”Pacific J. Math.,118, No. 2, 199–214 (1985).
E. P. Trofimchuk and S. I. Trofimchuk, “Pulse systems with fixed shock times in a general position: The existence and uniqueness of a solution; correctness of the Cauchy problem,”Ukr. Mat. Zh.,42, No. 2, 230–237 (1990).
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Translated from Ukrainskii Matematicheskii Zhumal, Vol. 45, No. 10, pp. 1390–1397, October, 1993.
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Rogovchenko, Y.V. Periodic solutions of pulse evolutionary systems with unbounded nonlinearities. Ukr Math J 45, 1560–1568 (1993). https://doi.org/10.1007/BF01571090
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DOI: https://doi.org/10.1007/BF01571090