Abstract
We consider possible methods for the reduction of a countable-point nonlinear boundary-value problem with nonlinear boundary condition on a segment to a finite-dimensional multipoint problem constructed on the basis of the original problem by the truncation method. The results obtained are illustrated by examples.
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REFERENCES
K. P. Persidskii, Infinite Systems of Differential Equations. Differential Equations in Nonlinear Spaces [in Russian], Nauka, Alma-Ata (1976).
A. M. Samoilenko and Yu. V. Teplinskii, Countable Systems of Differential Equations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1993).
O. M. Martynyuk, Investigation of Solutions of Boundary-Value Problems for Countable Systems of Nonlinear Differential Equations [in Ukrainian], Author’s Abstract of the Candidate-Degree Thesis (Physics and Mathematics), Kiev (1993).
Yu. V. Teplinskii and V. A. Nedokis, “Limit theorems in the theory of multipoint boundary-value problems, ” Ukr. Mat. Zh., 51, No.4, 519–531 (1999).
Yu. V. Teplins’kyi and V. A. Nedokis, “On countable-point boundary-value problems for countable systems of ordinary differential equations,” Nelin. Kolyvannya, No. 2, 252–266 (1999).
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).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 9, pp. 1203–1230, September, 2004.
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Samoilenko, A.M., Teplins’kyi, Y.V. & Nedokis, V.A. Truncation method for countable-point boundary-value problems in the space of bounded number sequences. Ukr Math J 56, 1429–1462 (2004). https://doi.org/10.1007/s11253-005-0126-6
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DOI: https://doi.org/10.1007/s11253-005-0126-6