On the multiplicity of eigenvalues of a fourth-order differential operator on a graph. (English. Russian original) Zbl 1509.34090
Differ. Equ. 58, No. 7, 869-876 (2022); translation from Differ. Uravn. 58, No. 7, 882-889 (2022).
Summary: We study the properties of eigenvalues of a boundary value problem for a fourth-order differential equation on a geometric graph modeling the elastic deformations of a system of rods elastically hinged at the joints. We establish the simplicity conditions for the points of the spectrum of the corresponding differential operator. Estimates for the multiplicity of eigenvalues are derived. These estimates are given in terms of the topological characteristics of the graph. The estimates are sharp within the framework of these concepts.
MSC:
| 34L15 | Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators |
| 34B45 | Boundary value problems on graphs and networks for ordinary differential equations |
| 47E05 | General theory of ordinary differential operators |
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