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RESEARCH PRODUCT

Eigenvalue Accumulation for Singular Sturm–Liouville Problems Nonlinear in the Spectral Parameter

Joseph P. Lutgen

subject

Nonlinear systemsymbols.namesakeApplied MathematicsMathematical analysissymbolsBoundary (topology)Sturm–Liouville theoryInterval (mathematics)Dirac operatorEigenvalues and eigenvectorsAnalysisMathematics

description

Abstract For certain singular Sturm–Liouville equations whose coefficients depend continuously on the spectral parameter λ in an interval Λ it is shown that accumulation/nonaccumulation of eigenvalues at an endpoint ν of Λ is essentially determined by oscillatory properties of the equation at the boundary λ = ν . As applications new results are obtained for the radial Dirac operator and the Klein–Gordon equation. Three other physical applications are also considered.

10.1006/jdeq.1999.3671http://dx.doi.org/10.1006/jdeq.1999.3671