Abstract
It is shown that the eigenvalues of the equation — ⋋Δu = V u on a graph G of finite total length |G|, where V ∈ L1(G) is nonnegative, under appropriate boundary conditions satisfy the inequality n 2⋋n ≤ |G| ∫ G Vdx independently of geometry of a given graph. Applications and generalizations of this result are also discussed.
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Dedicated to Olga Aleksandrovna Ladyzhenskaya to whom I am indebted for my formation as a mathematician
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Solomyak, M. (2002). On Eigenvalue Estimates for the Weighted Laplacian on Metric Graphs. In: Birman, M.S., Hildebrandt, S., Solonnikov, V.A., Uraltseva, N.N. (eds) Nonlinear Problems in Mathematical Physics and Related Topics I. International Mathematical Series, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0777-2_20
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DOI: https://doi.org/10.1007/978-1-4615-0777-2_20
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