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Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 2, Pages 238–244 (Mi timm825)  

This article is cited in 2 scientific papers (total in 2 papers)

On successive approximations of solutions of a singular Cauchy problem

N. A. Sidorova, D. N. Sidorovba

a Institute of Mathematics, Economics and Informatics of Irkutsk State University
b L. A. Melentiev Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences

Abstract: Solutions of the Cauchy problem for a differential equation with a Fredholm operator in the main part are constructed by successive approximations, which converge uniformly in a neighborhood of algebraic branch points. The leading term of the asymptotics is constructed with the help of the analytical theory of branching solutions of operator equations. It is employed as the initial approximation.

Keywords: Cauchy problem, Fredholm operator, branching of solutions, asymptotics, successive approximations.

Full text: PDF file (168 kB)
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UDC: 517.988.8
Received: 28.03.2011

Citation: N. A. Sidorov, D. N. Sidorov, “On successive approximations of solutions of a singular Cauchy problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 18, no. 2, 2012, 238–244

Citation in format AMSBIB
\Bibitem{SidSid12}
\by N.~A.~Sidorov, D.~N.~Sidorov
\paper On successive approximations of solutions of a~singular Cauchy problem
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2012
\vol 18
\issue 2
\pages 238--244
\mathnet{http://mi.mathnet.ru/timm825}
\elib{https://elibrary.ru/item.asp?id=17736203}


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    This publication is cited in the following articles:
    1. S. S. Orlov, “O razreshimosti integro-differentsialnykh uravnenii Volterra s fredgolmovym operatorom v glavnoi chasti”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 5:3 (2012), 73–93  mathnet
    2. Falaleev V M., Romanova O.A., Sinitsyn V A., Dreglea I A., Leont'ev R.Yu., Sidorov D.N., “on the Occasion of the 80Th Birthday of Professor N. a. Sidorov”, Bull. Irkutsk State Univ.-Ser. Math., 32 (2020), 134–143  crossref  mathscinet  zmath  isi
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