An Estimate on the Number of Bound States of Schr¨odinger Operators

This paper is concerned with the eigenvalue problem yDqV x..uslu on V and u<­V s0, where V is a bounded domain in R2 and V is a suitable function defined on V. We prove that the number of non-positive eigenvalues of the preceding problem is bounded by const. H V 1qlogqV .dx, where V is the Vy y y negative part of V.