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 The Bulletin of Irkutsk State University. Series Mathematics, 2012, Volume 5, Issue 1, Pages 80–95 (Mi iigum60)

Solution to the Volterra equations of the 1st kind with discontinuous kernels in the class of generalized functions

D. N. Sidorovab

a Irkutsk State University, 1, K. Marks St., Irkutsk, 664003
b Energy Systems Institute SB RAS, 130 Lermontov Str., Irkutsk, 664003

Abstract: Sufficient conditions for existence and uniqueness of solutions of the equations of Volterra equation of the 1st kind with a piecewise continuous kernels in the class of generalized functions with point support are derived. An asymptotic approximation of a parametric family of generalized solutions is constructed. A method of the regular part of the solution’s improvement employs the method of successive approximations.

Keywords: Volterra integral equations; discontinuous kernel; generalized solution; successive approximations.

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Citation: D. N. Sidorov, “Solution to the Volterra equations of the 1st kind with discontinuous kernels in the class of generalized functions”, The Bulletin of Irkutsk State University. Series Mathematics, 5:1 (2012), 80–95

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\Bibitem{Sid12} \by D.~N.~Sidorov \paper Solution to the Volterra equations of the 1st kind with discontinuous kernels in the class of generalized functions \jour The Bulletin of Irkutsk State University. Series Mathematics \yr 2012 \vol 5 \issue 1 \pages 80--95 \mathnet{http://mi.mathnet.ru/iigum60} 

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This publication is cited in the following articles:
1. E. V. Markova, D. N. Sidorov, “Integralnye uravneniya Volterra pervogo roda s kusochno-nepreryvnymi yadrami v teorii modelirovaniya razvivayuschikhsya sistem”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 5:2 (2012), 31–45
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