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.

中文翻译：

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具有参数的非线性方程的整体可解性

摘要

我们考虑从一个Banach空间到另一个Banach空间的平滑映射，并取决于属于拓扑空间的参数。在各种规律性假设下，获得了存在整体和半局部连续逆和隐函数的充分条件。我们考虑将这些结果应用于隐式函数的连续扩展问题以及平滑和连续紧凑映射的重合点问题。