Neutral set differential equations

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

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 3, page 593-615
  • ISSN: 0011-4642

Abstract

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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 D H X ( t ) = F ( t , X t , D H X t ) , X | [ - r , 0 ] = Ψ , where F : [ 0 , b ] × 𝒞 0 × 𝔏 0 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 , 𝒞 0 denotes the space of all continuous set-valued functions X from [ - r , 0 ] into K c ( E ) , 𝔏 0 1 is the space of all integrally bounded set-valued functions X : [ - r , 0 ] → K c ( E ) , Ψ ∈ 𝒞 0 and D H is the Hukuhara derivative. The continuous dependence of solutions on initial data and parameters is also studied.

How to cite

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Abbas, Umber, et al. "Neutral set differential equations." Czechoslovak Mathematical Journal 65.3 (2015): 593-615. <http://eudml.org/doc/271801>.

@article{Abbas2015,
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\begin\{equation*\} \{\left\lbrace \begin\{array\}\{ll\} D\_\{H\}X(t)=F(t,X\_\{t\},D\_\{H\}X\_\{t\}), \\ \hspace\{2.5pt\}X|\_\{[-r,0]\}=\Psi , \end\{array\}\right.\} \end\{equation*\} where $F\colon [0,b]\times \mathcal \{C\}_\{0\}\times \mathfrak \{L\}_\{0\}^\{1\}\rightarrow K_\{c\}(E)$ is a given function, $K_\{c\}(E)$ is the family of all nonempty compact and convex subsets of a separable Banach space $E$, $\mathcal \{C\}_\{0\}$ denotes the space of all continuous set-valued functions $X$ from $[-r,0]$ into $K_\{c\}(E)$, $\mathfrak \{L\}_\{0\}^\{1\}$ is the space of all integrally bounded set-valued functions $X\colon [-r,0]\rightarrow K_\{c\}(E)$, $\Psi \in \mathcal \{C\}_\{0\}$ and $D_\{H\}$ is the Hukuhara derivative. The continuous dependence of solutions on initial data and parameters is also studied.},
author = {Abbas, Umber, Lupulescu, Vasile, O'Regan, Donald, Younus, Awais},
journal = {Czechoslovak Mathematical Journal},
keywords = {neutral type; existence; uniqueness; continous dependence},
language = {eng},
number = {3},
pages = {593-615},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Neutral set differential equations},
url = {http://eudml.org/doc/271801},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Abbas, Umber
AU - Lupulescu, Vasile
AU - O'Regan, Donald
AU - Younus, Awais
TI - Neutral set differential equations
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 3
SP - 593
EP - 615
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\begin{equation*} {\left\lbrace \begin{array}{ll} D_{H}X(t)=F(t,X_{t},D_{H}X_{t}), \\ \hspace{2.5pt}X|_{[-r,0]}=\Psi , \end{array}\right.} \end{equation*} where $F\colon [0,b]\times \mathcal {C}_{0}\times \mathfrak {L}_{0}^{1}\rightarrow K_{c}(E)$ is a given function, $K_{c}(E)$ is the family of all nonempty compact and convex subsets of a separable Banach space $E$, $\mathcal {C}_{0}$ denotes the space of all continuous set-valued functions $X$ from $[-r,0]$ into $K_{c}(E)$, $\mathfrak {L}_{0}^{1}$ is the space of all integrally bounded set-valued functions $X\colon [-r,0]\rightarrow K_{c}(E)$, $\Psi \in \mathcal {C}_{0}$ and $D_{H}$ is the Hukuhara derivative. The continuous dependence of solutions on initial data and parameters is also studied.
LA - eng
KW - neutral type; existence; uniqueness; continous dependence
UR - http://eudml.org/doc/271801
ER -

References

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