The lower spectrum of Schrödinger operators

DOI10.1007/BF00250476zbMath0455.35046OpenAlexW1966866027MaRDI QIDQ1150093

U.-W. Schmincke

Publication date: 1981

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00250476

zbMATH Keywords

positive solutionsSchrödinger operatorsspectrumelliptic equationslower spectrum

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Estimates of eigenvalues in context of PDEs (35P15) Schrödinger operator, Schrödinger equation (35J10)

Related Items (12)

On the connection between Schrödinger and Dirichlet forms ⋮ Conditional oscillation of half-linear differential equations with coefficients having mean values ⋮ Integral averages and oscillation criteria for half-linear partial differential equation. ⋮ Oscillation criteria of Nehari-type for Sturm–Liouville operators and elliptic differential operators of second order and the lower spectrum ⋮ Unnamed Item ⋮ On the existence of nodal domains for elliptic differential operators ⋮ Oscillation of the half-linear PDE in general exterior domains -- the variational approach ⋮ Eigenvalues Below the Essential Spectra of Singular Elliptic Operators ⋮ Oscillation criteria for PDE with \(p\)-Laplacian via the Riccati technique ⋮ On the distribution of eigenvalues of Schrödinger operators ⋮ Elliptic equations without positive solutions ⋮ Conjugacy criteria for second order differential equations

Cites Work

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• Finiteness of the lower spectrum of Schrödinger operators
• The bound state of weakly coupled Schrödinger operators in one and two dimensions
• Positive solutions of elliptic equations
• Applications of a commutation formula
• Essential self-adjointness of Schrödinger operators bounded from below
• On the equivalence of two types of oscillation for elliptic operators
• Elliptic Partial Differential Equations of Second Order
• On Schrödinger's factorization method for Sturm-Liouville operators
• A Characterization of the Friedrichs Extension of Sturm-Liouville Operators

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