Abstract
We justify partial averaging schemes for quasidifferential equations that generalize the corresponding results for differential equations and inclusions.
References
A. I. Panasyuk and V. I. Panasyuk,Asymptotic Optimization of Nonlinear Control Systems [in Russian], Belorussia University, Minsk (1977).
A. A. Tolstonogov, “On solutions of the equation of the integral funnel of a differential inclusion,”Differents. Uravn.,20, No. 2, 358–359 (1984).
A. I. Panasyuk, “On quasidifferential equations in metric spaces,”Differents. Uravn.,21, No. 8, 1344–1353 (1985).
V. I. Zubov,Stability of Motion [in Russian], Vysshaya Shkola, Moscow (1984).
G. A. Stepan'yants,Theory of Dynamical Systems [in Russian], Mashinostroenie, Moscow (1985).
F. S. de Blasi and F. Iervolino, “Equazioni differentiali con soluzioni a valore compatto convesso,”Boll. Unione Mat. Ital.,2, No. 4–5, 491–501 (1969).
M. Hukuhara, “Sur l'application mesurables dont la valeur est un compact convexe,”Func. Ekvacioj, No. 10, 43–66 (1967).
M. Hukuhara, “Integration des applications mesurable dont la valeur est un compact convexe,”Funk. Ekvacioj, No. 10, 205–223 (1967).
A. V. Plotnikov, “Averaging of differential inclusions with Hukuhara's derivative”,Ukr. Mat. Zh.,41, No. 1, 121–125 (1989).
V. A. Plotnikov, “Partial averaging of differential inclusions,”Mat. Zametki,27, No. 6, 947–952 (1980).
V. A. Plotnikov, “Averaging method for differential inclusions and its applications to the problems of optimal control,”Differents. Uravn.,27, No. 8, 1427–1433 (1979).
V. A. Plotnikov,Asymptotic Methods in the Problems of Optimal Control [in Russian], Odessa University, Odessa (1976).
V. A. Plotnikov,Averaging Method in the Problems of Control [in Russian], Lybid', Kiev-Odessa (1992).
N. N. Bogolyubov and Yu. A. Mitropol'skii,Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).
A. N. Filatov,Asymptotic Methods in the Theory of Differential and Integro-Differential Equations [in Russian], Fan, Tashkent (1974).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 10, pp. 1442–1447, October, 1995.
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Plotnikov, V.A., Plotnikova, L.I. Partial averaging of quasidifferential equations in metric spaces. Ukr Math J 47, 1653–1659 (1995). https://doi.org/10.1007/BF01060167
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DOI: https://doi.org/10.1007/BF01060167