ON OBTAINING EFFECTIVE CONDITIONS FOR THE SOLVABILITY OF A SYSTEM OF FUNCTIONAL-DIFFERENTIAL EQUATIONS DETERMINATED ON A GEOMETRIC GRAPH-Reference-Cited by-同舟云学术

ON OBTAINING EFFECTIVE CONDITIONS FOR THE SOLVABILITY OF A SYSTEM OF FUNCTIONAL-DIFFERENTIAL EQUATIONS DETERMINATED ON A GEOMETRIC GRAPH

Published:2018 Issue:123 Volume: Page:531-538
ISSN:1810-0198
Container-title:Tambov University Reports. Series: Natural and Technical Sciences
language:
Short-container-title:Tamb. Un. Rep. Ser. Nat. Tech. Sci.

Author:

Plaksina Vera Pavlovna¹

Affiliation:

1. Perm National Research Polytechnic University

Abstract

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 Θ of disjoint segments of the real axis. The Azbelev’s W-method is applied to the system determined on the set Θ; what makes it possible to obtain effective conditions for the unique solvability of the original system. An example is given.

Publisher

Tambov State University - G.R. Derzhavin

Reference8 articles.

1. Pokornyy Yu.V., Penkin O.M., Pryadiev V.L., Borovskikh A.V., Lazarev K.P., Shabrov S.A. Differentsial’nye uravneniya na geometricheskikh grafakh [Differential Equations at Geometrical Graphs]. Moscow, Fizmatlit Publ., 2005, 272 p. (In Russian).

2. Pokornyy Yu.V., Bakhtina Zh.I., Zvereva M.B., Shabrov S.A. Ostsillyatsionnyy metod Shturma v spektral’nykh zadachakh [Schturm Oscillatory Method at Special Problems]. Moscow, Fizmatlit Publ., 2009, 192 p. (In Russian).

3. Azbelev N.V., Maksimov V.P., Rakhmatullina L.F. Vvedenie v teoriyu funktsional’no-differentsial’nykh uravneniy [Introduction to the Theory of Functional Differential Inclusions]. Moscow, Nauka Publ., 1991, 280 p. (In Russian).

4. Azbelev N.V., Maksimov V.P., Rakhmatullina L.F. Elementy sovremennoy teorii funktsional’no-differentsial’nykh uravneniy. Metody i prilozheniya [Elements of Modern Theory of Functional Differential Equations. Methods and Applications]. Moscow, Institute of Computer Science Publ., 2002, 384 p. (In Russian).

5. Plaksina V.P., Provotorova E.N. Ob odnom klasse kraevykh zadach dlya impul’snykh sistem [On one class of boundary value problems for impulse systems]. Differentsial’nye uravneniya – Differential Equations, 1988, vol. 24, no. 8, pp. 881-885. (In Russian).