$\bf{S^1}$-index theory for the Lorentz force equation
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915775317540864 |
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| author | Bereanu, Cristian Pîrvuceanu, Alexandru |
| author_facet | Bereanu, Cristian Pîrvuceanu, Alexandru |
| contents | In this paper we prove that the $S^1$-invariance of the Poincaré action functional associated to the Lorentz force equation gives the existence of multiple critical points which are periodic solutions with a fixed period. To do this, we prove an abstract multiplicity result which is based upon the Lusternik-Schnirelman method with the $S^1$-index. The corresponding result in the context of the Fadell-Rabinowitz index is proved in Ekeland and Lasry (Ann. Math., 112 (1980)). The main feature of our abstract result is that it allows us to consider nonsmooth functionals satisfying only a weak compactness condition well adapted to the Poincaré functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05015 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $\bf{S^1}$-index theory for the Lorentz force equation Bereanu, Cristian Pîrvuceanu, Alexandru Analysis of PDEs Classical Analysis and ODEs 58E05, 58E35, 34C25, 83A05, 70H40 In this paper we prove that the $S^1$-invariance of the Poincaré action functional associated to the Lorentz force equation gives the existence of multiple critical points which are periodic solutions with a fixed period. To do this, we prove an abstract multiplicity result which is based upon the Lusternik-Schnirelman method with the $S^1$-index. The corresponding result in the context of the Fadell-Rabinowitz index is proved in Ekeland and Lasry (Ann. Math., 112 (1980)). The main feature of our abstract result is that it allows us to consider nonsmooth functionals satisfying only a weak compactness condition well adapted to the Poincaré functional. |
| title | $\bf{S^1}$-index theory for the Lorentz force equation |
| topic | Analysis of PDEs Classical Analysis and ODEs 58E05, 58E35, 34C25, 83A05, 70H40 |
| url | https://arxiv.org/abs/2602.05015 |