Abstract and Applied Analysis (Jan 2014)
Asymptotic Behaviors of the Eigenvalues of Schrödinger Operator with Critical Potential
Abstract
We study the asymptotic behaviors of the discrete eigenvalue of Schrödinger operator P(λ)=P0+λV with P0=-Δ+qθ/r2. We obtain the leading terms of discrete eigenvalues of P(λ) when the eigenvalues tend to 0. In particular, we obtain the asymptotic behaviors of eigenvalues when (P0−α)−1 has singularity at α=0.