On the Existence of a Solution of a Boundary Value Problem on a Graph for a Nonlinear Equation of the Fourth Order-Reference-Cited by-同舟云学术

On the Existence of a Solution of a Boundary Value Problem on a Graph for a Nonlinear Equation of the Fourth Order

Published:2023-12-15 Issue:9 Volume:59 Page:1181-1190
ISSN:0374-0641
Container-title:Дифференциальные уравнения
language:
Short-container-title:Differencialʹnye uravneniâ

Author:

Kulaev R. Ch.¹,Urtaeva A. A.²

Affiliation:

1. Southern Mathematical Institute, Vladikavkaz Scientific Center, Russian Academy of Sciences, Vladikavkaz, 362025, Russia

2. Khetagurov North Ossetian State University, Vladikavkaz, 362025, Russia

Abstract

A fourth-order nonlinear differential equation on a network that is a model of a system of Euler–Bernoulli rods is considered. Based on the monotone iteration method, the existence of a solution of a boundary value problem on a graph for this equation is established using the positiveness of the Green’s function and the maximum principle for the corresponding linear differential equation. An example is given to illustrate the results.

Publisher

The Russian Academy of Sciences

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