The Green function of the boundary value problem on a star-shaped graph
type: Item
instance of: scholarly article
title: The Green function of the boundary value problem on a star-shaped graph
zbMATH Open document ID: 1279.34045
DOI: 10.3103/S1066369X13020060
author: R. Ch. Kulaev
published in: Russian Mathematics
publication date: 2013-04-10T00:00:00Z
review text: The author considers a planar graph consisting of three edges with one common vertex. He is interested in the sign of the Green function of the boundary value problem for a fourth-order equation. This problem models deformations of star-shaped coupled networks of beams. The author assumes that the network is fixed at each vertex, and all beams are rigidly jointed at their common vertex. He proves that the Green function is positive on diagonal squares and establishes a sufficient condition for its positivity inside its domain of definition.
reviewed by: Chuan-Fu Yang
Mathematics Subject Classification ID: 34B45
Mathematics Subject Classification ID: 34B27
zbMATH DE Number: 6152679
zbMATH Keywords: graph
zbMATH Keywords: network
zbMATH Keywords: differential equation on graph
zbMATH Keywords: Green function of problem on graph
MaRDI profile type: Publication
cites work: Q4933229
cites work: Q4664614
cites work: Q4934272
cites work: Control of networks of Euler-Bernoulli beams
cites work: Control of Planar Networks of Timoshenko Beams
full work available at URL: s1066369x13020060
OpenAlex ID: W2048061724
Recommended article: Q4846329
Recommended article: Q3455157
Recommended article: Q4695828
Recommended article: Solvability and Green's function of a degenerate boundary value problem on a graph
Recommended article: Q4318198
Recommended article: Q3979352
Recommended article: Q3642027
Recommended article: Green function solution of generalised boundary value problems
Recommended article: Green's functions for Stieltjes boundary problems
Recommended article: Q3810154
description: scientific article; zbMATH DE number 6152679