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Singular Dirac systems and Sturm-Liouville problems nonlinear in the spectral parameter. (English) Zbl 1012.34082

Here, the Dirac operator

H=-iα+β+V

acting in L 2 ( 3 ) 4 with a spherically symmetric potential V is studied. Under certain additional assumptions on V, the essential spectrum satisfies σ ess (H)=(-1,1). The authors investigate whether the endpoints -1 and 1 of the gap (-1,1) are accumulation points of discrete eigenvalues.

MSC:
34L40Particular ordinary differential operators
34L05General spectral theory for OD operators
34B07Linear boundary value problems with nonlinear dependence
34B16Singular nonlinear boundary value problems for ODE
34B24Sturm-Liouville theory
34B40Boundary value problems for ODE on infinite intervals