We establish necessary and sufficient conditions for the existence of solutions of weakly nonlinear degenerate boundary-value problems for systems of ordinary differential equations with a Noetherian operator in the linear part. We propose a convergent iterative procedure for finding solutions and establish the relationship between necessary and sufficient conditions.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 9, pp. 1174–1188, September, 2009.
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Boichuk, O.A., Shehda, L.M. Degenerate nonlinear boundary-value problems. Ukr Math J 61, 1387–1403 (2009). https://doi.org/10.1007/s11253-010-0284-z
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DOI: https://doi.org/10.1007/s11253-010-0284-z