Abstract:
In this paper, we prove the existence of infinitely many solutions of a stationary nonlinear Dirac equation on the Schwarzschild metric, outside a massive ball. These solutions are the critical points of a strongly indefinite functional. Thanks to a concavity property, we are able to construct a reduced functional, which is no longer strongly indefinite. We find critical points of this new functional using the Symmetric Mountain Pass Lemma. Note that, as A. Bachelot-Motet conjectured, these solutions vanish as the radius of the massive ball tends to the horizon radius of the metric.
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Received: 2 August 1999 / Accepted: 14 February 2000
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Paturel, E. A New Variational Principle for a Nonlinear Dirac Equation on the Schwarzschild Metric. Commun. Math. Phys. 213, 249–266 (2000). https://doi.org/10.1007/s002200000243
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DOI: https://doi.org/10.1007/s002200000243