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Bulletin of Irkutsk State University. Series Mathematics, 2012, Volume 5, Issue 1, Pages 80–95 (Mi iigum60)  
This article is cited in 1 scientific paper (total in 1 paper)

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
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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.
Document Type: Article
UDC: 517.968
Language: Russian
Citation: D. N. Sidorov, “Solution to the Volterra equations of the 1st kind with discontinuous kernels in the class of generalized functions”, Bulletin of Irkutsk State University. Series Mathematics, 5:1 (2012), 80–95
Citation in format AMSBIB
\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 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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