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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, Issue 11, Pages 62–74 (Mi vyuru47)  

Mathematical Modelling

Continuous and generalized solutions of singular integro-differential equations in Banach spaces

N. A. Sidorov, M. V. Falaleev

Irkutsk State University (Irkutsk, Russian Federation)

Abstract: Continuous and generalized solutions of singular equations in Banach spaces are studied. We apply Lyapunov–Schmidt's ideas and the generalized Jordan sets techniques and reduce partial differential-operator equations with the Fredholm operator in the main expression to regular problems. In addition the left and right regularizators of singular operators in Banach spaces and fundamental operators in the theory of generalized solutions of singular equations are constructed.

Keywords: singular PDE, regularizators, distributions, fundamental operator-function.

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UDC: 517.983.5
Received: 16.11.2011
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Citation: N. A. Sidorov, M. V. Falaleev, “Continuous and generalized solutions of singular integro-differential equations in Banach spaces”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, no. 11, 62–74

Citation in format AMSBIB
\Bibitem{SidFal12}
\by N.~A.~Sidorov, M.~V.~Falaleev
\paper Continuous and generalized solutions of singular integro-differential equations in Banach spaces
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2012
\issue 11
\pages 62--74
\mathnet{http://mi.mathnet.ru/vyuru47}


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