Abstract
We establish conditions for the existence and uniqueness of a periodic solution of one nonlinear difference equation.
References
A. Halanay and D. Wexler, Qualitative Theory of Impulsive Systems [Russian translation], Mir, Moscow (1971).
Ya. V. Bykov and V. G. Linenko, On Some Problems of the Qualitative Theory of Systems of Difference Equations [in Russian], Him, Frunze (1968).
Yu. A. Mitropol’skii, A. M. Samoilenko, and D. I. Martynyuk, Systems of Evolution Equations with Periodic and Quasiperiodic Coefficients [in Russian], Naukova Dumka, Kiev (1985).
A. N. Sharkovskii, Yu. L. Maistrenko, and E. Yu. Romanenko, Difference Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1986).
G. P. Pelyukh, “On the existence of periodic solutions of discrete difference equations and their properties,” Ukr. Mat. Zh., 46, No. 10, 1382–1387 (1994).
G. P. Pelyukh, “On periodic solutions of difference equations with continuous argument,” Ukr. Mat. Zh., 48, No. 1, 140–145 (1996).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 2, pp. 304–308, February, 1998.
This work was financially supported by the Foundation for Fundamental Research of the Ukrainian Committee for Science and Technology.
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Pelyukh, G.P. On periodic solutions of nonlinear difference equations in the critical case. Ukr Math J 50, 349–354 (1998). https://doi.org/10.1007/BF02513457
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DOI: https://doi.org/10.1007/BF02513457