A note on a global invertibility of mappings on $R^{n}$

TL;DR

This paper establishes sufficient conditions under which a strictly differentiable mapping from R^n to R^n is globally invertible, combining local invertibility criteria with non-smooth critical point theory.

Contribution

It introduces a novel approach by integrating classical local invertibility conditions with non-smooth critical point theory to ensure global invertibility.

Findings

Provides new sufficient conditions for global invertibility

Extends classical invertibility results to non-smooth settings

Bridges local invertibility with global properties using critical point theory

Abstract

We provide sufficient conditions for a mapping $f:R^{n}\rightarrow R^{n}$ to be a global diffeomorphism in case it is strictly (Hadamard) differentiable. We use classical local invertibility conditions together with the non-smooth critical point theory.