Inverse function theorem and extended differentiability in Banach spaces
type: Item
instance of: scholarly article
title: Inverse function theorem and extended differentiability in Banach spaces
zbMATH Open document ID: 0897.46026
published in: Russian Mathematics
publication date: 1996-08-21T00:00:00Z
review text: A version of the inverse function theorem is given for the situation, where the derivative is not invertible at the initial point. It is shown that under certain conditions locally ``extended'' solutions exist and the corresponding multi-valued mapping is ``extendedly'' differentiable in a sense defined by the same author in [``On differentiability of implicit function in Banach spaces'', Archives of Viniti, 2270 (1989)]. This is applied to a certain nonlinear elliptic equation without Gateaux differentiable solutions.
reviewed by: Andreas Kriegl
Mathematics Subject Classification ID: 46G05
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 898880
zbMATH Keywords: inverse function theorem
zbMATH Keywords: elliptic differential equations
zbMATH Keywords: multi-valued mapping
zbMATH Keywords: nonlinear elliptic equation
zbMATH Keywords: Gateaux differentiable solutions
author: S. Ya. Serovaiskii
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 898880