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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2109.00826 |
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| _version_ | 1866915691732402176 |
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| author | Mandel, Rainer |
| author_facet | Mandel, Rainer |
| contents | We prove the existence of a ground state and infinitely many geometrically distinct solutions for static nonlinear Maxwell's equations on $\mathbb{R}^3$. Our existence result relies on a variant of the Symmetric Mountain Pass Theorem that applies to periodic as well as vanishing nonlinearities. It is applied in a dual variational setting and thus provides an alternative approach with respect to the direct variational method introduced by Mederski. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_00826 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Dual variational methods for static Nonlinear Maxwell's Equations Mandel, Rainer Analysis of PDEs We prove the existence of a ground state and infinitely many geometrically distinct solutions for static nonlinear Maxwell's equations on $\mathbb{R}^3$. Our existence result relies on a variant of the Symmetric Mountain Pass Theorem that applies to periodic as well as vanishing nonlinearities. It is applied in a dual variational setting and thus provides an alternative approach with respect to the direct variational method introduced by Mederski. |
| title | Dual variational methods for static Nonlinear Maxwell's Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2109.00826 |