This article is cited in 2 papers

Comparison theorems for Green function of a fourth order boundary value problem on a graph

R. Ch. Kulaev<sup>ab

a</sup> Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
^b North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz, Russia

Abstract: In the work we develop the non-oscillation theory for fourth order equations on a geometric graph arising in modelling of rod junctions. The non-oscillation of an equation is defined in terms of the properties of a special fundamental system of solutions to the homogeneous equation. We describe the relation between non-oscillation property and the positivity of Green function to some classes of boundary value problems for fourth order equation on a graph.

Keywords: graph, differential equation on a graph, non-oscillation, Green function.

UDC: 517.927.5

MSC: 34C10

Received: 10.04.2015

 English version: Ufa Mathematical Journal, 2015, 7:4, 94–103

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