Abstract
Linear one-dimensional integrodifferentiat equations of second order with constant limits of integration are considered. Methods are developed for transforming these equations into equivalent Fredholm integral equations of second order. Thus we show that in order to correctly pose problems for this class of equations it is necessary to prescribe a number of linearly independent side conditions (initial, boundary, etc.) equal to the total order of the free differential expression. Theorems are formulated for the existence of solutions and the uniqueness of the solution to correctly posed problems. These problems are also briefly examined for other classes of integrodiffential equations (weighted equations, certain classes of nonlinear equation, etc.)
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Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 8–16, 1989.
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Kalaida, A.F. Linear one-dimensional integrodifferential problems. J Math Sci 67, 3035–3041 (1993). https://doi.org/10.1007/BF01098136
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DOI: https://doi.org/10.1007/BF01098136