Set Differential Equations in Fréchet Spaces

G. N. Galanis; T. G. Bhaskar; V. Lakshmikantham

doi:10.1515/JAA.2008.103

Published by De Gruyter June 9, 2010

Set Differential Equations in Fréchet Spaces

G. N. Galanis , T. G. Bhaskar and V. Lakshmikantham

From the journal Journal of Applied Analysis

https://doi.org/10.1515/JAA.2008.103

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Abstract

It is known that a Fréchet space 𝔽 can be realized as a projective limit of a sequence of Banach spaces . The space K_c(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 K_c(𝔽), we prove the local and global existence theorems for an initial value problem associated with a set differential equation.

Key words and phrases.: Set differential equations; Hukuhara derivative; projective limits; Fréchet spaces

Received: 2006-07-13

Revised: 2007-09-18

Published Online: 2010-06-09

Published in Print: 2008-June

Set Differential Equations in Fréchet Spaces

Abstract

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