Geodesic
On obtaining effective conditions for the solvability of a system of functional-differential equations determinated on a geometric graph
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 531-538

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

This paper is devoted to consideration of a boundary value problem for a system of functional differential equations determined on a geometric graph. The boundary conditions of the problem are determined by the conditions for the connection of the edges of the graph. There is an algorithm that reduces the system of equations on the graph to the system determined on the set $\Theta$ of disjoint segments of the real axis. The Azbelev's $W$-method is applied to the system determined on the set $\Theta,$ what makes it possible to obtain effective conditions for the unique solvability of the original system. An example is given.
Keywords: functional-differential equation, differential equation on a geometric graph. 
@article{VTAMU_2018_23_123_a23,
     author = {V. P. Plaksina},
     title = {On obtaining effective conditions for the solvability of a system of functional-differential equations determinated on a geometric graph},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {531--538},
     publisher = {mathdoc},
     volume = {23},
     number = {123},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a23/}
}
TY  - JOUR
AU  - V. P. Plaksina
TI  - On obtaining effective conditions for the solvability of a system of functional-differential equations determinated on a geometric graph
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2018
SP  - 531
EP  - 538
VL  - 23
IS  - 123
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a23/
LA  - ru
ID  - VTAMU_2018_23_123_a23
ER  - 
%0 Journal Article
%A V. P. Plaksina
%T On obtaining effective conditions for the solvability of a system of functional-differential equations determinated on a geometric graph
%J Vestnik rossijskih universitetov. Matematika
%D 2018
%P 531-538
%V 23
%N 123
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a23/
%G ru
%F VTAMU_2018_23_123_a23
V. P. Plaksina. On obtaining effective conditions for the solvability of a system of functional-differential equations determinated on a geometric graph. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 531-538. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a23/