On Principal Eigenvalues for Indefinite-Weight Elliptic Problems

Yehuda Pinchover ()
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Yehuda Pinchover: Technion-Israel Institute of Technology, Department of Mathematics

Chapter 6 in Spectral and Scattering Theory, 1998, pp 77-87 from Springer

Abstract: Abstract Consider the quantum mechanical system H μ=−Δ−μV in ℝd where μ ∈ ℝ is a spectral parameter and V ∈ C 0 ∞ (ℝd). It is well known that for d ≥ 3, the Schrödinger operator Hμ has no bound states provided that |μ| is sufficiently small. On the other hand, for d = 1, 2, B. Simon proved the following delicate result (see [35,37], and also the discussion in the Notes of [35]).

Keywords: Green Function; Elliptic Equation; Elliptic Operator; Harnack Inequality; Principal Eigenvalue (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4899-1552-8_6

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