An extension of the topological degree in Hilbert space

An extension of the topological degree in Hilbert space

We define classes of mappings of monotone type with respect to a given direct sum decomposition of the underlying Hilbert space H. The new classes are extensions of classes of mappings of monotone type familiar in the study of partial differential equations, for example, the class (S+) and the class...

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Main Authors: J. Berkovits, C. Fabry
Format: Article
Language:English
Published: Hindawi Limited 2005-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/AAA.2005.581
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spelling doaj-e4522656a3934a9b8566217c90c2625b2020-11-24T21:46:01ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092005-01-012005658159710.1155/AAA.2005.581An extension of the topological degree in Hilbert spaceJ. Berkovits0C. Fabry1Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, Oulu 90014, FinlandInstitut de Mathématique Pure et Appliquée, Université Catholique de Louvain, Chemin du Cyclotron 2, Louvain-la-Neuve 1348, BelgiumWe define classes of mappings of monotone type with respect to a given direct sum decomposition of the underlying Hilbert space H. The new classes are extensions of classes of mappings of monotone type familiar in the study of partial differential equations, for example, the class (S+) and the class of pseudomonotone mappings. We then construct an extension of the Leray-Schauder degree for mappings involving the above classes. As shown by (semi-abstract) examples, this extension of the degree should be useful in the study of semilinear equations, when the linear part has an infinite-dimensional kernel.http://dx.doi.org/10.1155/AAA.2005.581
collection DOAJ
language English
format Article
sources DOAJ
author J. Berkovits
C. Fabry
spellingShingle J. Berkovits
C. Fabry
An extension of the topological degree in Hilbert space
Abstract and Applied Analysis
author_facet J. Berkovits
C. Fabry
author_sort J. Berkovits
title An extension of the topological degree in Hilbert space
title_short An extension of the topological degree in Hilbert space
title_full An extension of the topological degree in Hilbert space
title_fullStr An extension of the topological degree in Hilbert space
title_full_unstemmed An extension of the topological degree in Hilbert space
title_sort extension of the topological degree in hilbert space
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2005-01-01
description We define classes of mappings of monotone type with respect to a given direct sum decomposition of the underlying Hilbert space H. The new classes are extensions of classes of mappings of monotone type familiar in the study of partial differential equations, for example, the class (S+) and the class of pseudomonotone mappings. We then construct an extension of the Leray-Schauder degree for mappings involving the above classes. As shown by (semi-abstract) examples, this extension of the degree should be useful in the study of semilinear equations, when the linear part has an infinite-dimensional kernel.
url http://dx.doi.org/10.1155/AAA.2005.581
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