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Solvability of the boundary-value problem for a variable-order differential equation on a geometric graph

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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 or 4 on dirrerent 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.

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Authors and Affiliations

  1. Voronezh Military Aviation Engineering Institute, Russia

    K. P. Lazarev & T. V. Beloglazova

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  1. K. P. Lazarev
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  2. T. V. Beloglazova
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__________

Translated from Matematicheskie Zametki, vol. 80, no. 1, 2006, pp. 60–68.

Original Russian Text Copyright © 2006 by K. P. Lazarev, T. V. Beloglazova.

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Lazarev, K.P., Beloglazova, T.V. Solvability of the boundary-value problem for a variable-order differential equation on a geometric graph. Math Notes 80, 57–64 (2006). https://doi.org/10.1007/s11006-006-0108-5

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  • DOI: https://doi.org/10.1007/s11006-006-0108-5

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