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Singular Dirac systems and Sturm-Liouville problems nonlinear in the spectral parameter. (English) Zbl 1012.34082
Here, the Dirac operator $$ H=-i\alpha \nabla +\beta+V$$ acting in $L^2(\bbfR^3)^4$ with a spherically symmetric potential $V$ is studied. Under certain additional assumptions on $V$, the essential spectrum satisfies $\sigma_{ess}(H)= \bbfR\backslash (-1,1)$. 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
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References:
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