Eigenvalues in gaps and decoupling by Neumann boundary conditions

Abstract

Continuing earlier investigations we show the existence of eigenvalues of Schrödinger operators H − λW, λ ϵ R , inside a spectral gap of H = − Δ + V, under suitable conditions on V and W. Our method of proof is based on a decoupling of regions in R v by means of Dirichlet or Neumann boundary conditions, where, in particular, the use of Neumann boundary conditions in the decoupling process leads to a new asymptotic results for eigenvalue counting functions.