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Viability result for higher-order functional differential inclusions


We prove, in separable Banach spaces, the existence of viable solutions for the following higher-order functional differential inclusion $$ x^{(k)}(t) \in F(t,T(t)x,x^{(1)}(t),...,x^{(k-1)}(t)),\quad\mbox{a.e. on }[0,\tau]. $$ We consider the case when the right-hand side is nonconvex and the constraint is moving.

Доводиться існування в сепарабельних банахових просторах розв'язків на всьому інтервалі для функціонально-диференціальних включень $$ x^{(k)}(t) \in F(t,T(t)x,x^{(1)}(t),...,x^{(k-1)}(t)),\quad\mbox{a.e. on }[0,\tau]. $$ Розглядається випадок неопуклої правої частини та рухомого обмеження.

Key words: Multifunction, measurability, selection, functional differential inclusion.

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Article Information

TitleViability result for higher-order functional differential inclusions
SourceMethods Funct. Anal. Topology, Vol. 26 (2020), no. 3, 189-200
MathSciNet   MR4165151
Milestones  Received 26/02/2020
CopyrightThe Author(s) 2020 (CC BY-SA)

Authors Information

Myelkebir Aitalioubrahim
University Sultan Moulay Slimane, Faculty polydisciplinary, BP 592, Mghila, Beni Mellal, Morocco

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Myelkebir Aitalioubrahim, Viability result for higher-order functional differential inclusions, Methods Funct. Anal. Topology 26 (2020), no. 3, 189-200.


@article {MFAT1391,
    AUTHOR = {Myelkebir Aitalioubrahim},
     TITLE = {Viability result for higher-order functional
differential inclusions},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {26},
      YEAR = {2020},
    NUMBER = {3},
     PAGES = {189-200},
      ISSN = {1029-3531},
  MRNUMBER = {MR4165151},
       DOI = {10.31392/MFAT-npu26_3.2020.01},
       URL = {},


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