Geodesic
On two-dimensional systems of Volterra integral equations of the first kind
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 3-10

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In this paper, we consider two-dimensional systems of Volterra integral equations of the first kind. The case where a system of integral equations of the second kind is obtained by differentiating the equations is well studied. We examine the case where this approach leads to a system of integral equations with an degenerate matrix of the principal part. We formulate sufficient conditions for the existence of a unique smooth solution in terms of matrix pencils.
Keywords: two-dimensional integral equation of Volterra type, integro-algebraic equation, matrix pencil. 
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     title = {On two-dimensional systems of {Volterra} integral equations of the first kind},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     volume = {208},
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M. V. Bulatov; L. S. Solovarova. On two-dimensional systems of Volterra integral equations of the first kind. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh International Spring Mathematical School "Modern Methods of the Theory of Boundary-Value Problems. Pontryagin Readings – XXXII”, Voronezh, May 3–9, 2021, Part 1, Tome 208 (2022), pp. 3-10. http://geodesic.mathdoc.fr/item/INTO_2022_208_a0/