Neutral set differential equations

Umber Abbas; Vasile Lupulescu; Donald O’Regan; Awais Younus

doi:10.1007/s10587-015-0199-9

Neutral set differential equations

Umber Abbas
, Vasile Lupulescu
, Donald O’Regan
, Awais Younus

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

5 Citations (Scopus)

Abstract

The aim of this paper is to establish an existence and uniqueness result for a class of the set functional differential equations of neutral type (Formula Presented.). where F: [0, b]×C₀ ×L₀ ¹→K_c(E) is a given function, K_c(E) is the family of all nonempty compact and convex subsets of a separable Banach space E, C₀ denotes the space of all continuous set-valued functions X from [−r, 0] into K_c(E), L₀ ¹ is the space of all integrally bounded set-valued functions X: [−r, 0] → K_c(E),Ψ ∈ C₀ and D_H is the Hukuhara derivative. The continuous dependence of solutions on initial data and parameters is also studied.

Original language	English
Pages (from-to)	593-615
Number of pages	23
Journal	Czechoslovak Mathematical Journal
Volume	65
Issue number	3
DOIs	https://doi.org/10.1007/s10587-015-0199-9
Publication status	Published - 1 Sep 2015

Keywords

continous dependence
existence
neutral type
uniqueness

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Abbas, U,Lupulescu, V,O'Regan, D,Younus, A

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10.1007/s10587-015-0199-9

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title = "Neutral set differential equations",

abstract = "The aim of this paper is to establish an existence and uniqueness result for a class of the set functional differential equations of neutral type (Formula Presented.). where F: [0, b]×C0 ×L0 1→Kc(E) is a given function, Kc(E) is the family of all nonempty compact and convex subsets of a separable Banach space E, C0 denotes the space of all continuous set-valued functions X from [−r, 0] into Kc(E), L0 1 is the space of all integrally bounded set-valued functions X: [−r, 0] → Kc(E),Ψ ∈ C0 and DH is the Hukuhara derivative. The continuous dependence of solutions on initial data and parameters is also studied.",

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doi = "10.1007/s10587-015-0199-9",

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TY - JOUR

T1 - Neutral set differential equations

AU - Abbas, Umber

AU - Lupulescu, Vasile

AU - O’Regan, Donald

AU - Younus, Awais

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Y1 - 2015/9/1

N2 - The aim of this paper is to establish an existence and uniqueness result for a class of the set functional differential equations of neutral type (Formula Presented.). where F: [0, b]×C0 ×L0 1→Kc(E) is a given function, Kc(E) is the family of all nonempty compact and convex subsets of a separable Banach space E, C0 denotes the space of all continuous set-valued functions X from [−r, 0] into Kc(E), L0 1 is the space of all integrally bounded set-valued functions X: [−r, 0] → Kc(E),Ψ ∈ C0 and DH is the Hukuhara derivative. The continuous dependence of solutions on initial data and parameters is also studied.

AB - The aim of this paper is to establish an existence and uniqueness result for a class of the set functional differential equations of neutral type (Formula Presented.). where F: [0, b]×C0 ×L0 1→Kc(E) is a given function, Kc(E) is the family of all nonempty compact and convex subsets of a separable Banach space E, C0 denotes the space of all continuous set-valued functions X from [−r, 0] into Kc(E), L0 1 is the space of all integrally bounded set-valued functions X: [−r, 0] → Kc(E),Ψ ∈ C0 and DH is the Hukuhara derivative. The continuous dependence of solutions on initial data and parameters is also studied.

KW - continous dependence

KW - existence

KW - neutral type

KW - uniqueness

UR - https://www.scopus.com/pages/publications/84944065445

U2 - 10.1007/s10587-015-0199-9

DO - 10.1007/s10587-015-0199-9

M3 - Article

SN - 0011-4642

VL - 65

SP - 593

EP - 615

JO - Czechoslovak Mathematical Journal

JF - Czechoslovak Mathematical Journal

IS - 3

ER -

Neutral set differential equations

Abstract

Keywords

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