Factor-analysis of nonlinear mappings: \(p\)-regularity theory
The authors consider the problem of solving a nonlinear equation of the form \(F(x)= 0\), where \(F: X\to Y\) is a sufficiently smooth mapping from a Banach space \(X\) to a Banach space \(Y\). They separate nonlinear mappings \(F\) and problems of the above form into two classes: regular -- those to which implicit function theorem arguments can be applied and irregular -- those to which it cannot. The main purpose of the paper is to show how to apply \(p\)-regularity theory to the description and investigation of singular mappings and to develop methods for finding solutions to related singular problems. The paper ends with many examples of applications.
scientific article; zbMATH DE number 2052053