RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. Vyssh. Uchebn. Zaved. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 2, Pages 56–66 (Mi ivm8775)  

This article is cited in 2 scientific papers (total in 2 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

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.

Full text: PDF file (223 kB)
References: PDF file   HTML file

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:2, 48–57

UDC: 517.927
Received: 19.12.2011

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
\Bibitem{Kul13}
\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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84878423759}


Linking options:
  • http://mi.mathnet.ru/eng/ivm8775
  • http://mi.mathnet.ru/eng/ivm/y2013/i2/p56

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. Ch. Kulaev, “O znake funktsii Grina kraevoi zadachi na grafe dlya uravneniya chetvertogo poryadka”, Vladikavk. matem. zhurn., 15:4 (2013), 19–29  mathnet
    2. R. Ch. Kulaev, “Disconjugacy of fourth-order equations on graphs”, Sb. Math., 206:12 (2015), 1731–1770  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
    Number of views:
    This page:155
    Full text:38
    References:24
    First page:10

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020