Abstract
The coefficient sufficient conditions for the existence of solutions and the iteration algorithm of constructing these solutions are obtained for weakly nonlinear boundary-value problems for systems of ordinary differential equations with pulse influence in the general case in which the number of boundary conditions does not coincide with the order of the differential system. The equation is derived for generating amplitudes of these boundary-value problems. This equation determines the amplitude of a solution, which can be regarded as generating for the required solution, and gives necessary conditions for the existence of this solution.
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A. M. Samoilenko and N. A. Perestyuk,Differential Equations with Pulse Influence [in Russian], Vyshcha Shkola, Kiev (1987).
A. A. Boichuk,Constructive Methods in the Analysis of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1990).
A. M. Samoilenko and A. A. Boichuk, “Linear Noetherian boundary-value problems for differential systems with pulse influence,“Ukr. Mat. Zh.,44, No 3, 582–586 (1992).
A. A. Boichuk, N. A. Perestyuk, and A. M. Samoilenko, “Periodic solutions of momentum differential systems for critical cases,“Diff. Uravn., No 9, 1516–1521 (1991).
I. G. Malkin,Some Problems in the Theory of Nonlinear Oscillations [in Russian], Gostekhisdat, Moscow (1956).
E. A. Grebennikov and Yu. A. Ryabov,Constructive Methods in the Analysis of Nonlinear Systems [in Russian], Nauka, Moscow (1979).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 2, pp. 221–225, February, 1993.
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Boichuk, A.A., Khrashchevskaya, R.F. Weakly nonlinear boundary-value problems for differential systems with pulse influence. Ukr Math J 45, 235–240 (1993). https://doi.org/10.1007/BF01060978
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DOI: https://doi.org/10.1007/BF01060978