A Generalized Palais-Smale Condition in the Fréchet space setting

Abstract

We extend the Palais-Smale condition to Keller's $C_c^1$-functionals on Fréchet 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.

arXiv commentIn 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

Cited by in corpus (1)

• On the existence of a global diffeomorphism between Fréchet spaces