Nonlinear equations with operators satisfying generalized Lipschitz conditions in scales
type: Item
instance of: scholarly article
title: Nonlinear equations with operators satisfying generalized Lipschitz conditions in scales
zbMATH Open document ID: 0937.47061
DOI: 10.4171/ZAA/882
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2000-06-13T00:00:00Z
full work available at URL: https://eudml.org/doc/48415
review text: Summary: By means of the contraction principle we prove existence, uniqueness and stability of solutions for nonlinear equations \(u+ G_0[D,u]+ L(G_1[D, u],G_2[D, u])= f\) in a Banach space \(E\), where \(G_0\), \(G_1\), \(G_2\) satisfy Lipschitz conditions in scales of norms, \(L\) is a bilinear operator and \(D\) is a data parameter. The theory is applicable for inverse problems of memory identification and generalized convolution equations of the second kind.
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 1331699
zbMATH Keywords: contraction principle
zbMATH Keywords: uniqueness
zbMATH Keywords: stability
zbMATH Keywords: solutions for nonlinear equations
zbMATH Keywords: Lipschitz conditions in scales of norms
zbMATH Keywords: bilinear operator
zbMATH Keywords: generalized convolution equations of the second kind
author: Jaan Janno
MaRDI profile type: Publication
cites work: Inverse problems of memory reconstruction
cites work: On a Regularization Method for the Autoconvolution Equation
cites work: On a class of multilinear operator equations
cites work: Inverse problems for identification of memory kernels in thermo- and poro-viscoelasticity
cites work: Q4888291
cites work: On a class of nonlinear convolution equations
OpenAlex ID: W2126873327
description: scientific article; zbMATH DE number 1331699