Izv. Vyssh. Uchebn. Zaved. Mat., 2013, Number 2, Pages 56–66
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
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.
graph, network, differential equation on graph, Green function of problem on graph.
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Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:2, 48–57
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
\paper The Green function of the boundary value problem on a~star-shaped graph
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\jour Russian Math. (Iz. VUZ)
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This publication is cited in the following articles:
R. Ch. Kulaev, “O znake funktsii Grina kraevoi zadachi na grafe dlya uravneniya chetvertogo poryadka”, Vladikavk. matem. zhurn., 15:4 (2013), 19–29
R. Ch. Kulaev, “Disconjugacy of fourth-order equations on graphs”, Sb. Math., 206:12 (2015), 1731–1770
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