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Matematicheskie Zametki, 2006, Volume 80, Issue 1, Pages 60–68
DOI: https://doi.org/10.4213/mzm2780 (Mi mzm2780) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Solvability of the Boundary-Value Problem for a Variable-Order Differential Equation on a Geometric Graph

K. P. Lazarev, T. V. Beloglazova

Voronezh State University
Full-text PDF (496 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm2780
Abstract: The solvability of the boundary-value problem for a string-beam model is studied. The model is described by an equation of orders 2 and 4 on different edges of an arbitrary graph. Criteria for the problem to be degenerate and nondegenerate are obtained; in particular, it is proved that the nondegeneracy of the problem is equivalent to the maximum principle.
Keywords: geometric graph (network), ordinary differential equation on a graph, boundary-value problem, nondegeneracy, degeneracy, maximum principle.
Received: 23.12.2004
Revised: 05.09.2005
English version:
Mathematical Notes, 2006, Volume 80, Issue 1, Pages 57–64
DOI: https://doi.org/10.1007/s11006-006-0108-5
Bibliographic databases:
UDC: 517.927
Language: Russian
Citation: K. P. Lazarev, T. V. Beloglazova, “Solvability of the Boundary-Value Problem for a Variable-Order Differential Equation on a Geometric Graph”, Mat. Zametki, 80:1 (2006), 60–68; Math. Notes, 80:1 (2006), 57–64
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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