Relative oscillation -- non-oscillation criteria for perturbed periodic Dirac systems

DOI10.1006/jmaa.2000.6821zbMath0977.34076OpenAlexW2000458602MaRDI QIDQ1577948

Karl Michael Schmidt

Publication date: 27 November 2000

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.6821

zbMATH Keywords

radial solutionsDirac operatoreigenvalue estimatesnonoscillation criteria

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Estimates of eigenvalues in context of PDEs (35P15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Related Items

Exceptional coupling constants for the Coulomb-Dirac operator with anomalous magnetic moment ⋮ Relative oscillation theory for Dirac operators ⋮ Relative oscillation theory, weighted zeros of the Wronskian, and the spectral shift function ⋮ The extraordinary spectral properties of radially periodic Schrödinger operators ⋮ Eigenvalues in gaps of perturbed periodic Dirac operators: Numerical evidence

Cites Work

• Absolutely continuous spectra of perturbed periodic Hamiltonian systems
• Spectral theory of ordinary differential operators
• The discrete spectrum of perturbed differential operators of arbitrary order with periodic matrix coefficients
• Accumulation of discrete eigenvalues of the radial Dirac operator
• Critical coupling constants and eigenvalue asymptotics of perturbed periodic Sturm-Liouville operators
• Remarks on the spectrum of Dirac operators
• Oscillation of the perturbed Hill equation and the lower spectrum of radially periodic Schrödinger operators in the plane
• Perturbative Oscillation Criteria and Hardy-Type Ineqalities
• Renormalized oscillation theory for Dirac operators
• On the number of eigenvalues in the spectral gap of a Dirac system
• Dense point spectrum and absolutely continuous spectrum in spherically symmetric Dirac operators
• On the oscillatory behavior of the solutions of second order linear differential equations
• The spectrum of singular boundary problems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item