Geodesic
Integro-differential equations with degeneration in Banach spaces and it's applications in mathematical theory of elasticity
The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 1, pp. 118-134

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Cauchy problem for linear integro-differential operator equation with degenerated differential part of high order and convolutional type Volterra integral term is considered in article. Fundamental operator-function of integro-differential operator, appropriated of examining equation, is constructed, Cauchy problem generalized (in class of distributios with left-bounded support) and classical ($N$ times strongly continuously differentiable) solutions existence and uniqueness theorems are proved. Obtaining results are applied to the investigation of initial boundary value problems, arised in mathematical theory of elasticity.
Keywords: Banach space, Fredholm operator, fundamental operator-function.
Mots-clés : Jordan set, distribution 
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     title = {Integro-differential equations with degeneration in {Banach} spaces and it's applications in mathematical theory of elasticity},
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M. V. Falaleev; S. S. Orlov. Integro-differential equations with degeneration in Banach spaces and it's applications in mathematical theory of elasticity. The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 1, pp. 118-134. http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a10/