Abstract
We prove the existence of a solution and obtain an estimate for the error of the averaging method for a multifrequency system with linearly transformed argument and integral boundary conditions.
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REFERENCES
A. M. Samoilenko and R. I. Petryshyn, Multifrequency Oscillations of Nonlinear Systems [in Ukrainian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1998).
Ya. I. Bigun, "Averaging of a multifrequency boundary-value problem with linearly transformed argument," Ukr. Mat. Zh., 52, No. 3, 291–299 (2000).
R. I. Petryshyn and Ya. R. Petryshyn, "Averaging of boundary-value problems for systems of differential equations with slow and fast variables," Nelin. Kolyvannya, No. 1, 51–65 (1998).
V. A. Plotnikov, Averaging Method in Control Problems [in Russian], Lybid, Kiev-Odessa (1992).
A. M. Samoilenko and N. I. Ronto, Numerical-Analytic Methods in the Theory of Boundary-Value Problems for Ordinary Differential Equations [in Russian], Naukova Dumka, Kiev (1992).
N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Introduction to the Theory of Functional-Differential Equations [in Russian], Nauka, Moscow (1991).
A. A. Boichuk, V. F. Zhuravlev, and A. M. Samoilenko, Generalized Inverse Operators and Noether Boundary-Value Problems [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1995).
Ya. I. Bigun and A. M. Samoilenko, "Justification of the averaging principle for multifrequency systems of differential equations with delay," Differents. Uravn., 35, No. 1, 8–14 (1999).
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Bigun, Y.I. Averaging of Oscillation Systems with Delay and Integral Boundary Conditions. Ukrainian Mathematical Journal 56, 318–326 (2004). https://doi.org/10.1023/B:UKMA.0000036105.41652.9c
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DOI: https://doi.org/10.1023/B:UKMA.0000036105.41652.9c