Abstract
If Ñ(Ω, λ) is the number of eigenvalues of −Δ in a domain Ω In a suitable Rieinannian manifold of dimension n, we derive bounds of the form Ñ (Ω,λ)≤ Dnλn/2 |Ω| for all Ω, λ, n, Likewise, if Nα (V) is the number of nonpositive eigenvalues of −Δ + V(x) which are ≤ α ≤ 0, then Nα(V)≤ LnʃM [V − α]Stack− n/2 for all α and V and n ≥ 3.
1980 Mathematics Subject Classification 35P15.
Work supported by U.S. National Foundation grants PHYS-7825390 and INT 78-01160.
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Lieb, E.H. (2005). The Number of Bound States of One-Body Schroedincer Operators and the Weyl Problem. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27056-6_18
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