Set Differential Equations in Fréchet Spaces

It is known that a Fréchet space 𝔽 can be realized as a projective limit of a sequence of Banach spaces . The space Kc (𝔽) of all compact, convex subsets of a Fréchet space, 𝔽, is realized as a projective limit of the semilinear metric spaces . Using the notion of Hukuhara derivative for maps with v...

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Bibliographic Details
Published inJournal of applied analysis Vol. 14; no. 1; pp. 103 - 113
Main Authors Galanis, G. N., Bhaskar, T. G., Lakshmikantham, V.
Format Journal Article
LanguageEnglish
Published Walter de Gruyter GmbH & Co. KG 01.06.2008
Subjects
Fréchet spaces
Hukuhara derivative
projective limits
Set differential equations
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Summary:It is known that a Fréchet space 𝔽 can be realized as a projective limit of a sequence of Banach spaces . The space Kc (𝔽) of all compact, convex subsets of a Fréchet space, 𝔽, is realized as a projective limit of the semilinear metric spaces . Using the notion of Hukuhara derivative for maps with values in Kc (𝔽), we prove the local and global existence theorems for an initial value problem associated with a set differential equation.
Bibliography:jaa.2008.103.pdf
ark:/67375/QT4-FZ4N5T6C-R
ArticleID:JAA.14.1.103
istex:E426ECB9B41DCB2E1110DFF349CFB315AFEFD193
ISSN:1425-6908
1869-6082
DOI:10.1515/JAA.2008.103