Abstract

For nonlinear mappings acting in Banach spaces, we examine inverse and implicit function theorems under various smoothness assumptions. For various regularity (normality) conditions imposed on such mappings, we prove that the corresponding equations have solutions under any sufficiently small (in the norm) completely continuous perturbations. A priori estimates for these solutions are obtained.

中文翻译：

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完全连续扰动下非线性方程的稳定可解性

摘要

对于作用于Banach空间的非线性映射，我们研究了各种光滑度假设下的逆函数和隐函数定理。对于施加于此类映射的各种正则（正则）条件，我们证明了相应的等式具有在任何足够小的（范数）完全连续扰动下的解。获得这些解决方案的先验估计。