We propose a method for the investigation and solution of linear boundary-value problems for the Fredholm integrodifferential equations based on the partition of the interval and introduction of additional parameters. Every partition of the interval is associated with a homogeneous Fredholm integral equation of the second kind. The definition of regular partitions is presented. It is shown that the set of regular partitions is nonempty. A criterion for the solvability of the analyzed problem is established and an algorithm for finding its solutions is constructed.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 8, pp. 1074–1091, August, 2014.
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Dzhumabaev, D.S. Necessary and Sufficient Conditions for the Solvability of Linear Boundary-Value Problems for the Fredholm Integrodifferential Equations. Ukr Math J 66, 1200–1219 (2015). https://doi.org/10.1007/s11253-015-1003-6
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DOI: https://doi.org/10.1007/s11253-015-1003-6