This article is cited in 13 papers

Expansion in eigenfunctions of the Sturm–Liouville problem on a graph bundle

V. V. Provotorov

Voronezh State University

Abstract: In this paper we consider the applicability of the Fourier method for partial differential equations on spatial grids (we choose a bundle graph as a model). This leads to an important problem, namely, to the expansion of a given function in eigenfunctions of the corresponding Sturm–Liouville problem on a grid. We study a model problem which describes a symmetric case, when one considers physically identical one-dimensional continuums on the bundle graph. Such problems arise, for example, in the modeling of oscillating processes of an elastic mast with supporting elastic ties.

Keywords: boundary-value problem on a graph, eigenfunctions, the Green function, completeness of system of eigenfunctions, expansion in eigenfunctions.

UDC: 517.9

Received: 06.10.2006

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2008, 52:3, 45–57

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