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Set Differential Equations in Fréchet Spaces
-
G. N. Galanis
Published/Copyright:
June 9, 2010
Abstract
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.
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
© Heldermann Verlag
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Keywords for this article
Set differential equations;
Hukuhara derivative;
projective limits;
Fréchet spaces
Articles in the same Issue
- Finite Partitions of Topological Groups into Congruent Thick Subsets
- Derivatives of Markov Kernels and Their Jordan Decomposition
- Sufficiency and Duality in Control Problems with Generalized Invexity
- Koebe Domains for the Classes of Functions with Ranges Included in Given Sets
- Upper and Lower Solutions Method for Fourth-Order Periodic Boundary Value Problems
- Efficiency and Duality for Generalized Convex Multiobjective Programming
- General Mixed Vector F-Implicit Complementarity Problems in Banach Spaces
- Modelling and Products of Singularities in Colombeau's Algebra
- Set Differential Equations in Fréchet Spaces
- Positive Solutions for a Class of Nonresonant m-Point Boundary Value Problems
- Second Order Duality in Multiobjective Programming
