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A New Variational Principle for a Nonlinear Dirac Equation on the Schwarzschild Metric

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Date
2000
Dewey
Analyse
Sujet
nonlinear Dirac equation
Journal issue
Communications in Mathematical Physics
Volume
213
Number
2
Publication date
2000
Article pages
249-266
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s002200000243
URI
https://basepub.dauphine.fr/handle/123456789/6510
Collections
  • CEREMADE : Publications
Metadata
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Author
Paturel, Eric
Type
Article accepté pour publication ou publié
Abstract (EN)
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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