A Global Diffeomorphism Theorem for Fr\'{e}chet spaces
Differential Geometry
2023-08-01 v2
Abstract
We give sufficient conditions for a -local diffeomorphism between Fr\'{e}chet spaces to be a global one. We extend the Clarke's theory of generalized gradients to the more general setting of Fr\'{e}chet spaces. As a consequence, we define the Chang Palais-Smale condition for Lipschitz functions and show that a function which is bounded below and satisfies the Chang Palais-Smale condition at all levels is coercive. We prove a version of the mountain pass theorem for Lipschitz maps in the Fr\'{e}chet setting and show that along with the Chang Palais-Smale condition we can obtain a global diffeomorphism theorem.
Cite
@article{arxiv.1903.05162,
title = {A Global Diffeomorphism Theorem for Fr\'{e}chet spaces},
author = {Kaveh Eftekharinasab},
journal= {arXiv preprint arXiv:1903.05162},
year = {2023}
}