Factor-analysis of nonlinear mappings: \(p\)-regularity theory
type: Item
instance of: scholarly article
title: Factor-analysis of nonlinear mappings: \(p\)-regularity theory
zbMATH Open document ID: 1053.58004
author: J. E. Marsden
author: A. Tret'yakov
published in: Communications on Pure and Applied Analysis
publication date: 2004-03-07T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 58C15
Mathematics Subject Classification ID: 58K05
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 37G10
Mathematics Subject Classification ID: 49K27
Mathematics Subject Classification ID: 46N10
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 65J15
zbMATH DE Number: 2052053
zbMATH Keywords: \(p\)-regularity
zbMATH Keywords: nonlinear mapping
zbMATH Keywords: singularity
zbMATH Keywords: bifurcation
zbMATH Keywords: factor operator
zbMATH Keywords: optimality condition
zbMATH Keywords: implicit function
zbMATH Keywords: numerical method
zbMATH Keywords: differential equations
reviewed by: Vasil G. Angelov
MaRDI profile type: Publication
full work available at URL: cpaa.2003.2.425
OpenAlex ID: W2121209716
DOI: 10.3934/CPAA.2003.2.425
description: scientific article; zbMATH DE number 2052053