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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.10457 |
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| _version_ | 1866916948624801792 |
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| author | Ortega, Rafael Urena, Antonio J. |
| author_facet | Ortega, Rafael Urena, Antonio J. |
| contents | Given a real valued function having a nondegenerate compact manifold of critical points, some of these points survive under small $C^2$ perturbations. This is a well-known result in critical point theory. In 1986 Weinstein obtained the analogous conclusions when the perturbation is only $C^2$ and the ambient space is a finite dimensional manifold. In this work we present a complete proof for $C^1$ perturbations in infinite dimensional Hilbert spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10457 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $C^1$ perturbations of a continuum of critical points Ortega, Rafael Urena, Antonio J. Functional Analysis 58E05, 58E30 Given a real valued function having a nondegenerate compact manifold of critical points, some of these points survive under small $C^2$ perturbations. This is a well-known result in critical point theory. In 1986 Weinstein obtained the analogous conclusions when the perturbation is only $C^2$ and the ambient space is a finite dimensional manifold. In this work we present a complete proof for $C^1$ perturbations in infinite dimensional Hilbert spaces. |
| title | $C^1$ perturbations of a continuum of critical points |
| topic | Functional Analysis 58E05, 58E30 |
| url | https://arxiv.org/abs/2509.10457 |