Geodesic
Integro-differential equations with Fredholm operator by the derivative of the higest order in Banach spaces and it's applications
The Bulletin of Irkutsk State University. Series Mathematics, Tome 5 (2012) no. 2, pp. 90-102 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper the Cauchy problem for integro-differential equation in Banach spaces with Fredholm operator in main part is investigated by the methods of the theory of fundamental operator-functions. The fundamental operator-function is constructed, and constructiv formula for the generalized solution in the class of distributions with left-bounded support is obtained. The conditions for the coincidence of classical and generalized solutions are described. The abstract results are illustrated by examples of the Cauchy problem for a system of integro-differential equations of two-contour circuit and the Cauchy–Dirichlet problem of the mathematical theory of viscoelasticity.
Keywords: Banach spaces, generalized function, Fredholm operator, fundamental operator-function.
Mots-clés : Jordan set 
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M. V. Falaleev. Integro-differential equations with Fredholm operator by the derivative of the higest order in Banach spaces and it's applications. The Bulletin of Irkutsk State University. Series Mathematics, Tome 5 (2012) no. 2, pp. 90-102. http://geodesic.mathdoc.fr/item/IIGUM_2012_5_2_a8/

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