We study multiple eigenvalues of a magnetic Aharonov–Bohm operator with Dirichlet boundary conditions in a planar domain. In particular, we study the structure of the set of the couples position of the pole-circulation which keep fixed the multiplicity of a double eigenvalue of the operator with the pole at the origin and half-integer circulation. We provide sufficient conditions for which this set is made of an isolated point. The result confirms and validates a lot of numerical simulations available in preexisting literature
Abatangelo, L., Nys, M. (2018). On multiple eigenvalues for Aharonov–Bohm operators in planar domains. NONLINEAR ANALYSIS, 169, 1-37 [10.1016/j.na.2017.11.010].
On multiple eigenvalues for Aharonov–Bohm operators in planar domains
Abatangelo, Laura;
2018
Abstract
We study multiple eigenvalues of a magnetic Aharonov–Bohm operator with Dirichlet boundary conditions in a planar domain. In particular, we study the structure of the set of the couples position of the pole-circulation which keep fixed the multiplicity of a double eigenvalue of the operator with the pole at the origin and half-integer circulation. We provide sufficient conditions for which this set is made of an isolated point. The result confirms and validates a lot of numerical simulations available in preexisting literature
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