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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

##### MSC:
 47F05 General theory of partial differential operators (should also be assigned at least one other classification number in Section 47-XX) 35J10 Schrödinger operator, Schrödinger equation
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##### References:
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