On the existence of a global diffeomorphism between Fr\'echet spaces

TL;DR

This paper establishes conditions under which a global diffeomorphism exists between tame Fréchet spaces, utilizing a specialized Mountain Pass Theorem to achieve the main result.

Contribution

It introduces sufficient conditions for global diffeomorphisms between tame Fréchet spaces and proves a new version of the Mountain Pass Theorem for this context.

Findings

Sufficient conditions for global diffeomorphisms between tame Fréchet spaces.

A new version of the Mountain Pass Theorem applicable to tame Fréchet spaces.

Proof of the main theorem using the adapted Mountain Pass Theorem.

Abstract

We provide sufficient conditions for the existence of a global diffeomorphism between tame Fr\'{e}chet spaces. We prove a version of the Mountain Pass Theorem which is a key ingredient in the proof of the main theorem.