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On the classical and generalized solutions of boundary-value problems for difference-differential equations with variable coefficients

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Abstract

The first boundary-value problem for second-order difference-differential equations with variable coefficients on a finite interval (0, d) is considered. The following question is studied: Under what conditions will the boundary-value problem for a difference-differential equation have a classical solution for an arbitrary continuous right-hand side? It is proved that a necessary and sufficient condition for the existence of a classical solution is that certain coefficients of the difference operators on the orbits generated by the shifts be equal to zero.

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia, Moscow, Russia

    D. A. Neverova & A. L. Skubachevskii

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  1. D. A. Neverova
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  2. A. L. Skubachevskii
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Correspondence to D. A. Neverova.

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Original Russian Text © D. A. Neverova, A. L. Skubachevskii, 2013, published in Matematicheskie Zametki, 2013, Vol. 94, No. 5, pp. 702–719.

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Neverova, D.A., Skubachevskii, A.L. On the classical and generalized solutions of boundary-value problems for difference-differential equations with variable coefficients. Math Notes 94, 653–667 (2013). https://doi.org/10.1134/S0001434613110072

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