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Gauge Invariant Eigenvalue Problems in $\mathbb {R}^n$ and in $\mathbb {R}^n_+$
1999
Transactions of the American Mathematical Society
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This paper is devoted to the study of the eigenvalue problems for the Ginzburg-Landau operator in the entire plane R 2 and in the half plane R 2 + . The estimates for the eigenvalues are obtained and the existence of the associate eigenfunctions is proved when curl A is a non-zero constant. These results are very useful for estimating the first eigenvalue of the Ginzburg-Landau operator with a gauge-invariant boundary condition in a bounded domain, which is closely related to estimates of the
doi:10.1090/s0002-9947-99-02516-7
fatcat:kj7zvyhv7jbn3fgzmtubeub4q4