Abstract
We consider an operator (variable hysteron) used to describe a nonstationary hysteresis nonlinearity (whose characteristics vary under the action of external forces) according to the Krasnosel’skii-Pokrovskii scheme. Sufficient conditions under which the operator is defined for the inputs from the class of functions H 1[t 0, T] satisfying the Lipschitz condition in the segment [t 0, T] are established.
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M. A. Krasnosel’skii and A. V. Pokrovskii, Systems with Hysteresis [in Russian], Nauka, Moscow (1983).
R. E. Kalman, R. L. Falb, and M. A. Arbib, Topics in Mathematical System Theory, McGraw-Hill, New York (1969).
M. A. Krasnosel’skii and A. V. Pokrovskii, “Vibrostability of solutions of differential equations,” Dokl. Akad. Nauk SSSR, 195, No. 3, 544–547 (1970).
M. A. Krasnosel’skii and V. V. Chernorutskii, “On one class of hysteresis nonlinearities,” Dokl. Akad. Nauk SSSR, 305, No. 5, 1065–1069 (1989).
V. V. Chernorutskii and M. A. Krasnosel’skii, “Hysteresis systems with variable characteristics,” Nonlin. Anal. Theor., Meth. Appl., 18, No. 6, 543–557 (1992).
V. K. Dzyadyk, Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).
V. I. Borzdyko, Differential Equations with Complex Nonlinearities [in Russian], Doctoral-Degree Thesis (Physics and Mathematics), Dushanbe (2000).
G. M. Fikhtengol’ts, A Course in Differential and Integral Calculus [in Russian], Vol. 1, Nauka, Moscow (1960).
V. I. Borzdyko, “Variable hysteron,” Dokl. Ros. Akad. Nauk, 324, No. 2, 269–272 (1992).
V. I. Borzdyko, “Nonlinear nonstationary systems with hysteresis,” Avtomat. Telemekh., No. 5, 20–26 (1994).
V. I. Borzdyko, “Variable hysteron,” in: Abstr. of the Scientific School-Seminar “Simulation and Investigation of Physical Processes” [in Russian], (Kiev, May 1991), p. 9.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 3, pp. 295–309, March, 2008.
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Borzdyko, V.I. Hysteresis nonstationary nonlinearities. Ukr Math J 60, 339–356 (2008). https://doi.org/10.1007/s11253-008-0062-3
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DOI: https://doi.org/10.1007/s11253-008-0062-3