We study the limit with respect to a parameter in the uniform norm for the solutions of general boundary-value problems for systems of linear ordinary differential equations of the first order. A generalization of the Kiguradze theorem (1987) to this class of problems is obtained. The conditions imposed on the asymptotic behavior of the coefficients of systems are weakened as much as possible. Sufficient conditions for the uniform convergence of Green matrices to the Green matrix of the limit boundary-value problem are also established.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 1, pp. 70–81, January, 2013.
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Kodlyuk, T.I., Mikhailets, V.A. & Reva, N.V. Limit theorems for one-dimensional boundary-value problems. Ukr Math J 65, 77–90 (2013). https://doi.org/10.1007/s11253-013-0766-x
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DOI: https://doi.org/10.1007/s11253-013-0766-x