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arXiv · 2509.10457

$C^1$ perturbations of a continuum of critical points

Rafael Ortega·Antonio J. Urena
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Abstract

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.

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Rafael Ortega, Antonio J. Urena. 2025-07-15. $C^1$ perturbations of a continuum of critical points. https://arxiv.org/abs/2509.10457

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