Application of Methods of Ordinary Differential Equations to Global Inverse Function Theorems

Abstract

We obtain a global inverse function theorem guaranteeing that if a smooth mapping of finite-dimensional spaces is uniformly nonsingular, then it has a smooth right inverse. Global implicit function theorems are obtained guaranteeing the existence and continuity of a global implicit function under the condition that the mappings in question are uniformly nonsingular. The local Lipschitz property and the smoothness of the global implicit function are studied. The results are generalized to the case of mappings of Hilbert spaces.