A new infinite-dimensional Linking theorem with application to a system of coupled Poisson equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916961281114112 |
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| author | Songo, Ablanvi Colin, Fabrice |
| author_facet | Songo, Ablanvi Colin, Fabrice |
| contents | Using the minimax technique from the critical point theory, which consists in constructing or transforming a suitable class of applications such that a critical value $c$ of a functional $f$ can be characterized as a minimax value over this class, we establish a new natural infinite-dimensional linking theorem for strongly indefinite functionals by using the $τ-$topology of Kryszewski and Szulkin. Our result is a generalization of the classical linking theorem \cite[Theorem 2.21]{Wi}. As an application, we obtain the existence of a nontrivial solution to a system of coupled Poisson equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_17563 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new infinite-dimensional Linking theorem with application to a system of coupled Poisson equations Songo, Ablanvi Colin, Fabrice Analysis of PDEs 35J05, 35J61, 35J91, 58E05 Using the minimax technique from the critical point theory, which consists in constructing or transforming a suitable class of applications such that a critical value $c$ of a functional $f$ can be characterized as a minimax value over this class, we establish a new natural infinite-dimensional linking theorem for strongly indefinite functionals by using the $τ-$topology of Kryszewski and Szulkin. Our result is a generalization of the classical linking theorem \cite[Theorem 2.21]{Wi}. As an application, we obtain the existence of a nontrivial solution to a system of coupled Poisson equations. |
| title | A new infinite-dimensional Linking theorem with application to a system of coupled Poisson equations |
| topic | Analysis of PDEs 35J05, 35J61, 35J91, 58E05 |
| url | https://arxiv.org/abs/2506.17563 |