2002/01/03 by Michael Solomyak · 1 citation
Mathematics · #math.SP #math.CO #msc:34L15 #msc:46E35 #msc:45P05
published as In the book: INTERNATIONAL MATHEMATICAL SERIES. Nonlinear Problems in Mathematical Physics and Related Topics I. In Honor of Professor Ladyzhenskaya. Kluwer Academic/Plenum Publishers, 2002, p.327 - 348
arxiv created 2002/01/03 · arxiv updated 2009/11/30
Eigenvalue behavior for the equation -λy"=Vu on the edges of a graph G of final total length, with a non-negative weight function V and under the Kirchhoff matching conditions at the vertices and zero boundary condition at at least one point of G, is studied. It is shown that the eigenvalues satisfy an inequality which involves the length |G| and the total mass corresponding to V but otherwise does not depend on the graph. Applications and generalizations of this result are also discussed.