$C^1$ perturbations of a continuum of critical points
Functional Analysis
2025-09-16 v1
Abstract
Given a real valued function having a nondegenerate compact manifold of critical points, some of these points survive under small perturbations. This is a well-known result in critical point theory. In 1986 Weinstein obtained the analogous conclusions when the perturbation is only and the ambient space is a finite dimensional manifold. In this work we present a complete proof for perturbations in infinite dimensional Hilbert spaces.
Keywords
Cite
@article{arxiv.2509.10457,
title = {$C^1$ perturbations of a continuum of critical points},
author = {Rafael Ortega and Antonio J. Urena},
journal= {arXiv preprint arXiv:2509.10457},
year = {2025}
}