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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{IIGUM_2012_5_2_a8,
     author = {M. V. Falaleev},
     title = {Integro-differential equations with {Fredholm} operator by the derivative of the higest order in {Banach} spaces and it's applications},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {90--102},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2012_5_2_a8/}
}
TY  - JOUR
AU  - M. V. Falaleev
TI  - Integro-differential equations with Fredholm operator by the derivative of the higest order in Banach spaces and it's applications
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2012
SP  - 90
EP  - 102
VL  - 5
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2012_5_2_a8/
LA  - ru
ID  - IIGUM_2012_5_2_a8
ER  - 
%0 Journal Article
%A M. V. Falaleev
%T Integro-differential equations with Fredholm operator by the derivative of the higest order in Banach spaces and it's applications
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2012
%P 90-102
%V 5
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIGUM_2012_5_2_a8/
%G ru
%F IIGUM_2012_5_2_a8
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/