ON A GLOBAL IMPLICIT FUNCTION THEOREM FOR LOCALLY LIPSCHITZ MAPS VIA NON-SMOOTH CRITICAL POINT THEORY

摘要

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.