Eigenvalue ratios for Schr?dinger operators with indefinite potentials

摘要

AbstractWe consider the Schr?dinger equation?y′′+q(x)y=λy,on a finite interval with Dirichlet boundary conditions, whereq(x)is of indefinite sign. In the case of symmetric potentials, we prove the optimal lower boundλnλ1≥n2(resp. upper boundλnλ