On coincidence index for multivalued perturbations of nonlinear Fredholm maps and some applications
type: Item
instance of: scholarly article
title: On coincidence index for multivalued perturbations of nonlinear Fredholm maps and some applications
zbMATH Open document ID: 1038.47042
DOI: 10.1155/S1085337502002853
author: Pietro Zecca
author: Valerii V. Obukhovskij
author: V. G. Zvyagin
published in: Abstract and Applied Analysis
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/50782
review text: To investigate problems of nonlinear analysis, often topological methods for special operators are used. Therefore, it is the aim of this paper to define a nonoriented coincidence index for compact, fundamentally restrictible, and condensing multivalued perturbations of a map which is nonlinear Fredholm of nonnegative index on the set of coincidence points. The basis of the construction is the coincidence index of an \(s\)-admissible pair defined as an element of the Rohlin-Thom ring of bordisms; the main facts of this theory are briefly presented. In the first step, the authors consider single-valued perturbations. They define the coincidence index and prove the coincidence point-, the homotopic invariance- and the map restriction property. Using these results, the coincidence index is defined and analogous properties are proved for multivalued perturbations. In the following chapter, the coincidence index for the desired maps is defined, topological invariance and the coincidence property are proved. In the last chapter, the authors apply their results to an optimal controllability problem for a system governed by a second-order integro-differential equation and prove the existence of a solution.
reviewed by: Marianne Reichert
Mathematics Subject Classification ID: 47H11
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 49J22
Mathematics Subject Classification ID: 58B15
zbMATH DE Number: 1780536
zbMATH Keywords: coincidence index
zbMATH Keywords: nonlinear Fredholm maps
zbMATH Keywords: topological invariance
zbMATH Keywords: optimal controllability
MaRDI profile type: Publication
OpenAlex ID: W2024843532
description: scientific article; zbMATH DE number 1780536