Topological characteristics and the Fredholm analysis in nonlinear problems
type: Item
instance of: scholarly article
title: Topological characteristics and the Fredholm analysis in nonlinear problems
zbMATH Open document ID: 0840.58006
author: Yu. G. Borisovich
published in: Russian Mathematics
publication date: 1995-11-05T00:00:00Z
review text: The author presents several new results of Voronezh mathematicians. Section I contains a resume of the results by the author and O. V. Kunakovskaya. They extend a construction from the Arnold theory of boundary singularities to the infinite-dimensional case. It follows a theorem concerning problems of longitudinal acoustic waves in a crystal with a given elastic modulus tensor. Section II contains an exposition of results by Zvyagin, Sapronov, Ratiner etc. devoted to the problems of nonlinear theory of elasticity, problems of differential geometry, etc. In the last third Section a boundary value problem for the Monge-Ampère equation is formulated. Finally other applications of Fredholm theory of nonlinear mappings are enumerated.
Mathematics Subject Classification ID: 58B15
zbMATH DE Number: 795230
zbMATH Keywords: nonlinear mappings
zbMATH Keywords: Fredholm operators
zbMATH Keywords: crystals
zbMATH Keywords: boundary singularities
zbMATH Keywords: acoustic waves
zbMATH Keywords: nonlinear theory of elasticity
zbMATH Keywords: Monge-Ampère equation
reviewed by: Vasil G. Angelov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 795230