On a global implicit function theorem for locally Lipschitz maps via non-smooth critical point theory

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. Applications to algebraic equations are given.

Keywords: Mountain pass theorem, global implicit function, locally Lipschitz function, non-smooth global inversion theorem