Geodesic
Multiperiodic solutions of quasilinear systems of integro-differential equations with $D_c$-operator and $\epsilon$-period of hereditarity
Eurasian mathematical journal, Tome 13 (2022) no. 1, pp. 86-100

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

We investigate a quasilinear system of partial integro-differential equations with the operator of differentiation in the direction of a vector field, which describes the process of hereditary propagation with an $\epsilon$-period of heredity. Under some conditions on the input data, conditions for the solvability of the initial problem for a quasilinear system of integro-differential equations are obtained. On this basis, sufficient conditions for the existence of multiperiodic solutions of integro-differential systems are found under the exponential dichotomy additional assumption on the corresponding homogeneous integro-differential system. The unique solvability of an operator equation in the space of smooth multiperiodic functions is proved, to which the main question under consideration reduces. Thus, sufficient conditions are established for the existence of a unique multiperiodical in all time variables solution of a quasilinear system of integro-differential equations with the differentiation operator in the directions of a vector field and a finite period of hereditarity. 
@article{EMJ_2022_13_1_a6,
     author = {Zh. A. Sartabanov and G. M. Aitenova and G. A. Abdikalikova},
     title = {Multiperiodic solutions of quasilinear systems of integro-differential equations with $D_c$-operator and $\epsilon$-period of hereditarity},
     journal = {Eurasian mathematical journal},
     pages = {86--100},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2022_13_1_a6/}
}
TY  - JOUR
AU  - Zh. A. Sartabanov
AU  - G. M. Aitenova
AU  - G. A. Abdikalikova
TI  - Multiperiodic solutions of quasilinear systems of integro-differential equations with $D_c$-operator and $\epsilon$-period of hereditarity
JO  - Eurasian mathematical journal
PY  - 2022
SP  - 86
EP  - 100
VL  - 13
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2022_13_1_a6/
LA  - en
ID  - EMJ_2022_13_1_a6
ER  - 
%0 Journal Article
%A Zh. A. Sartabanov
%A G. M. Aitenova
%A G. A. Abdikalikova
%T Multiperiodic solutions of quasilinear systems of integro-differential equations with $D_c$-operator and $\epsilon$-period of hereditarity
%J Eurasian mathematical journal
%D 2022
%P 86-100
%V 13
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2022_13_1_a6/
%G en
%F EMJ_2022_13_1_a6
Zh. A. Sartabanov; G. M. Aitenova; G. A. Abdikalikova. Multiperiodic solutions of quasilinear systems of integro-differential equations with $D_c$-operator and $\epsilon$-period of hereditarity. Eurasian mathematical journal, Tome 13 (2022) no. 1, pp. 86-100. http://geodesic.mathdoc.fr/item/EMJ_2022_13_1_a6/