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We investigate spectral stability of vortex solutions of the Gross-Pitaevskiiequation, a mean-field approximation for Bose-Einstein condensates (BEC) in aneffectively two-dimensional axisymmetric harmonic trap. We study eigenvalues ofthe linearization both rigorously and through computation of the Evansfunction, a sensitive and robust technique whose use we justify mathematically.The absence of unstable eigenvalues is justified a posteriori through use ofthe Krein signature of purely imaginary eigenvalues, which also can be used tosignificantly reduce computational effort. In particular, we prove generalbasic continuation results on Krein signature for finite systems of eigenvaluesin infinite-dimensional problems.

Spectral stability of vortices in two-dimensional Bose-Einstein condensates via the Evans function and Krein signature