A Generalized Palais-Smale Condition in the Fr\'echet space setting
Differential Geometry
2025-06-03 v4
Abstract
We extend the Palais-Smale condition to Keller's -functionals on Fr\'{e}chet spaces. Using this condition together with Ekeland's variational principle, we obtain some results regarding the existence of minima. In this setting, we prove that the Palais-Smale condition for functionals bounded below implies the coercivity.
Keywords
Cite
@article{arxiv.1410.5638,
title = {A Generalized Palais-Smale Condition in the Fr\'echet space setting},
author = {Kaveh Eftekharinasab},
journal= {arXiv preprint arXiv:1410.5638},
year = {2025}
}
Comments
In the published version of this paper, we defined the Palais-Smale condition on Frechet manifolds using the concept of the $\beta$-cotangent bundle. However, this definition has since been shown to be invalid. Therefore, in this updated version, we have removed the Palais-Smale definition and all related results concerning Frechet manifolds. we also add some new result to the published version