On a global implicit function theorem for locally Lipschitz maps via nonsmooth critical point theory

TL;DR

This paper extends the implicit function theorem to non-smooth, locally Lipschitz functions using nonsmooth critical point theory, providing a broader framework for global inversion results.

Contribution

It introduces a non-smooth global implicit function theorem based on nonsmooth analysis, expanding the classical theory to locally Lipschitz maps.

Findings

Established a non-smooth global implicit function theorem

Compared various global inversion theorems

Extended classical results to nonsmooth settings

Abstract

We prove a non-smooth generalization of the global implicit function theorem. More precisely we use the non-smooth local implicit function theorem and the non-smooth critical point theory in order to prove a non-smooth global implicit function theorem for locally Lipschitz functions. A comparison between several global inversion theorems is discussed.