Eigenvalue branches of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H). (English) Zbl 0676.47032

The authors study the eigenvalue branches of the Schrödinger operator H-\(\lambda\) W in a gap of \(\sigma\) (H). In particular, they consider questions of asymptotic distributions of eigenvalues and bounds on the number of branches. They study the asymptotics for \(N_-\) (eigenvalue distribution function) for \(W\geq 0\) and \(W(x)\sim c| x|^{- \alpha}\) as \(| x| \to \infty\), in the case where W is supported in a finite ball, and where \(W=W_+-W_-\) with \(W_{\pm}\geq 0\).
Reviewer: R.Salvi


47F05 General theory of partial differential operators
35J10 Schrödinger operator, Schrödinger equation
Full Text: DOI


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