We study the problem of finding conditions for the existence of solutions of weakly nonlinear Noetherian boundary-value problems for systems of ordinary differential equations and the construction of these solutions. A new iterative procedure with accelerated convergence is proposed for the construction of solutions of a weakly nonlinear Noetherian boundary-value problem for a system of ordinary differential equations in the critical case.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1587–1601, December, 2008.
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Boichuk, A.A., Chuiko, S.M. Method of accelerated convergence for the construction of solutions of a Noetherian boundary-value problem. Ukr Math J 60, 1861–1877 (2008). https://doi.org/10.1007/s11253-009-0176-2
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DOI: https://doi.org/10.1007/s11253-009-0176-2