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Study of the Solvability of Some Volterra-Type Integral and Integro-Differential Equations of Third Kind

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Abstract

For Volterra integral equations of the third kind and for Volterra-type integrodifferential equations of the third kind, theorems on the existence of solutions in Sobolev spaces (i.e., regular solutions) are proved. The proofs are based on the theory of boundary value problems for degenerate ordinary differential equations and on the theory of boundary value problems for parabolic equations with a changing evolution direction.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    A. I. Kozhanov

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  1. A. I. Kozhanov
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Correspondence to A. I. Kozhanov.

Additional information

Original Russian Text © A.I. Kozhanov, 2018, published in Doklady Akademii Nauk, 2018, Vol. 478, No. 3, pp. 262–265.

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Kozhanov, A.I. Study of the Solvability of Some Volterra-Type Integral and Integro-Differential Equations of Third Kind. Dokl. Math. 97, 38–41 (2018). https://doi.org/10.1134/S106456241801012X

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  • DOI: https://doi.org/10.1134/S106456241801012X

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