Optimal lower estimates for eigenvalue ratios of Schrodinger operators and vibrating strings

摘要

We obtain optimal lower estimates for the eigenvalue ratios (lambda m/lambda n) All of Dirichlet and Neumann, Schrodinger operators with nonpositive potentials and Dirichlet vibrating string problems with concave and positive densities. Our results supplement those of Ashbaugh-Benguria [2] and M. J. Huang [5].