Abstract:
In this article we obtain lower bounds for the minimum eigenvalue of a fourth-order differential operator on a metric graph, which is a model of a planar system of thin rods. In this way, we establish an analogue of the Picone identity for a fourth-order equation on a network. As an application of this identity, we formulate Sturm type comparison theorem for a fourth-order equation on a graph. Acknowledgements The work was carried out with the financial support of the Ministry of Science and Higher Education of the Russian Federation. Agreement no 075-02-2024-1447.
Keywords:eigenvalue, quantum graph, network equation, fourth order equation.
