Literature cited
A. Halanay, “An averaging method for systems of differential equations with lagging argument,” Rev. Math. Pures Appl., Acad. Roumanian P. R.,4, No. 3 (1959).
V. P. Rubanik, “The basis of the applicability of the averaging principle to systems of differential-difference equations,” in: Scientific Yearbook (1959) [in Russian], Chernovits. Gosuniv., Chernovtsy (1960).
I. Fodchuk, “Some questions in the theory of differential equations with lagging argument,” Author's Abstract of Candidate's Dissertation [in Russian], Inst. Matem. Akad. Nauk UkrSSR (1962).
P. Rubanik and V. I. Fodchuk, “On an averaging method for systems with lag,” Vsesoyuzn. Mezhvuz. Konf. po Teorii i Primen. Diff. Urav. s Otkl. Arg. [All-Union Interuniversity Conference on the Theory and Application of Differential Equations with Perturbed Arguments], Chernovtsy (1965).
N. N. Bogoliubov and I. A. Mitropolski, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York (1962).
V. P. Rubanik and V. I. Fodchuk, “On the existence and properties of abounded solution of a system of quasi-linear differential-difference equations,” Ukr. Matem. Zh.,14, No. 1 (1962).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 24, No. 1, pp. 49–56, January–February, 1972.
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Mitropol'skii, Y.A., Fodchuk, V.I. The second Bogolyubov theorem on the averaging method for differential equations with lagging argument. Ukr Math J 24, 38–44 (1972). https://doi.org/10.1007/BF01089120
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DOI: https://doi.org/10.1007/BF01089120