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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2013, Number 2, Pages 56–66 (Mi ivm8775)  
This article is cited in 9 scientific papers (total in 9 papers)

The Green function of the boundary value problem on a star-shaped graph

R. Ch. Kulaev

Department of Operator Theory, Southern Mathematical Institute, Vladikavkaz Scientific Center of Russian Academy of Sciences, Vladikavkaz, Republic of Northern Osetiya-Alaniya, Russia
Full-text PDF (223 kB) Citations (9)
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Abstract: We consider a planar graph consisting of three edges with one common vertex. We are interested in the sign of the Green function of the boundary value problem for a forth-order equation. This problem models deformations of star-shaped coupled networks of beams. We assume that the network is fixed at each vertex, and all beams are rigidly jointed at their common vertex. We prove that the Green function is positive on diagonal squares and establish a sufficient condition for its positivity inside its definition domain.
Keywords: graph, network, differential equation on graph, Green function of problem on graph.
Received: 19.12.2011
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, Volume 57, Issue 2, Pages 48–57
DOI: https://doi.org/10.3103/S1066369X13020060
Bibliographic databases:
Document Type: Article
UDC: 517.927
Language: Russian
Citation: R. Ch. Kulaev, “The Green function of the boundary value problem on a star-shaped graph”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 2, 56–66; Russian Math. (Iz. VUZ), 57:2 (2013), 48–57
Citation in format AMSBIB
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\by R.~Ch.~Kulaev
\paper The Green function of the boundary value problem on a~star-shaped graph
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2013
\issue 2
\pages 56--66
\mathnet{http://mi.mathnet.ru/ivm8775}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2013
\vol 57
\issue 2
\pages 48--57
\crossref{https://doi.org/10.3103/S1066369X13020060}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84878423759}
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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