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Existence results for second-order neutral stochastic equations driven by Rosenblatt process


Abstract

In this paper we consider a class of second-order impulsive stochastic functional differential equations driven simultaneously by a Rosenblatt process and a standard Brownian motion in a Hilbert space. We prove an existence and uniqueness result under non-Lipschitz condition which is weaker than Lipschitz one and we establish some conditions ensuring the controllability for the mild solution by means of the Banach fixed point principle. At the end we provide a practical example in order to illustrate the viability of our result.

Розглянуто клас імпульсних стохастичних функціонально-диференціальних рівнянь другого порядку, які керуються процесом Розенблата і стандартним броунівський рухом у ґільбертовому просторі одночасно за умови, яка є слабкішою за умови Ліпшица. Також встановлено умови керованості для помірного розв'язку за допомоги принципу Банаха про нерухому точку. Наведено приклад з практики, що ілюструє отримані результати.

Key words: Controllability, Second-Order Stochastic System, Cosine Family, Rosenblatt process, Non-Lipschitz condition.


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Article Information

TitleExistence results for second-order neutral stochastic equations driven by Rosenblatt process
SourceMethods Funct. Anal. Topology, Vol. 27 (2021), no. 4, 384-400
DOI10.31392/MFAT-npu26_4.2021.11
MathSciNet   MR4425717
Milestones  Received 22/11/2020; Revised 14/04/2021
CopyrightThe Author(s) 2021 (CC BY-SA)

Authors Information

Rakia Ahmed Yahia
Laboratoire des Math´ematiques et leurs interactions "MELILAB". Abdelhafid Boussouf University Centre, Mila 43000, Algeria

Abbes Benchaabane
Laboratory of Analysis and Control of Differential Equations "ACED". Univ. 8 May 1945 Guelma, Algeria

Halim Zeghdoudi
Laboratory of Analysis and Control of Differential Equations "ACED". Univ. 8 May 1945 Guelma, Algeria


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Citation Example

Rakia Ahmed Yahia, Abbes Benchaabane, and Halim Zeghdoudi, Existence results for second-order neutral stochastic equations driven by Rosenblatt process, Methods Funct. Anal. Topology 27 (2021), no. 4, 384-400.


BibTex

@article {MFAT1701,
    AUTHOR = {Rakia Ahmed Yahia and Abbes Benchaabane and Halim Zeghdoudi},
     TITLE = {Existence results for second-order neutral stochastic
equations driven by Rosenblatt process},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {27},
      YEAR = {2021},
    NUMBER = {4},
     PAGES = {384-400},
      ISSN = {1029-3531},
  MRNUMBER = {MR4425717},
       DOI = {10.31392/MFAT-npu26_4.2021.11},
       URL = {http://mfat.imath.kiev.ua/article/?id=1701},
}


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