Set Differential Equations in Fréchet Spaces

Galanis, George; Bhaskar, T. Gnana; Lakshmikantham, V.

doi:10.1515/jaa.2008.103

Cited by 14 publications

(8 citation statements)

References 2 publications

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“…O'Regan and Xian [89] proved fixed point theorems for maps and multivalued maps between Fréchet spaces, using projective limits and the classical Banach theory. Further recent work on set valued maps between Fréchet spaces can be found in Galanis et al [61,62,88] and Bakowska and Gabor [10].…”

Section: Hypercyclicity Propertiesmentioning

confidence: 99%

A review of some recent work on hypercyclicity

Dodson

2012

Preprint

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Even linear operators on infinite-dimensional spaces can display interesting dynamical properties and yield important links among functional analysis, differential and global geometry and dynamical systems, with a wide range of applications. In particular, hypercyclicity is an essentially infinite-dimensional property, when iterations of the operator generate a dense subspace. A Fréchet space admits a hypercyclic operator if and only if it is separable and infinite-dimensional. However, by considering the semigroups generated by multiples of operators, it is possible to obtain hypercyclic behaviour on finite dimensional spaces. This article gives a brief review of some recent work on hypercyclicity of operators on Banach, Hilbert and Fréchet spaces. MSC: 58B25 58A05 47A16, 47B37

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Section: Hypercyclicity Propertiesmentioning

confidence: 99%

A review of some recent work on hypercyclicity

Dodson

2012

Preprint

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“…O'Regan and Xian [41] proved fixed point theorems for maps and multivalued maps between Fréchet spaces, using projective limits and the classical Banach theory. Further recent work on set valued maps between Fréchet spaces can be found in Galanis et al [27,28,40] and Bakowska and Gabor [6].…”

Section: Hypercyclicitymentioning

confidence: 99%

Some recent work in Frechet geometry

Dodson

2011

Preprint

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Some recent work in Fréchet geometry is briefly reviewed. In particular an earlier result on the structure of second tangent bundles in the finite dimensional case was extended to infinite dimensional Banach manifolds and Fréchet manifolds that could be represented as projective limits of Banach manifolds. This led to further results concerning the characterization of second tangent bundles and differential equations in the more general Fréchet structure needed for applications. A summary is given of recent results on hypercyclicity of operators on Fréchet spaces. MSC: 58B25 58A05 47A16, 47B37

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“…One can although mention several works on differential inclusions involving at some point Fréchet spaces, e.g. [43] or [27], and also the papers [22], [23] where set differential equations using the notion of Hukuhara derivative have been considered. In all previously mentioned papers, such a space is viewed as a projective limit of a sequence of Banach spaces.…”

Section: Introductionmentioning

confidence: 99%

Set valued integrability in non separable Fréchet spaces and applications

Piazza¹,

Marraffa²,

Satco³

2016

Mathematica Slovaca

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Abstract. We focus on measurability and integrability for set valued functions in non-necessarily separable Fréchet spaces. We prove some properties concerning the equivalence between different classes of measurable multifunctions. We also provide useful characterizations of Pettis set-valued integrability in the announced framework. Finally, we indicate applications to Volterra integral inclusions.

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Set Differential Equations in Fréchet Spaces

Cited by 14 publications

References 2 publications

A review of some recent work on hypercyclicity

A review of some recent work on hypercyclicity

Some recent work in Frechet geometry

Set valued integrability in non separable Fréchet spaces and applications

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