On Global Solvability of Nonlinear Equations with Parameters
Aram Vladimirovich Arutyunov, Sergey Evgenyevich Zhukovskiy · Doklady Mathematics · 2021
Abstract We consider smooth mappings acting from one Banach space to another and depending on a parameter belonging to a topological space. Under various regularity assumptions, sufficient conditions for the existence of global and semilocal continuous inverse and implicit functions are obtained. We consider applications of these results to the problem of continuous extension of implicit functions and to the problem of coincidence points of smooth and continuous compact mappings.