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.
Full Text
Article Information
| Title | Existence results for second-order neutral stochastic
equations driven by Rosenblatt process |
| Source | Methods Funct. Anal. Topology, Vol. 27 (2021), no. 4, 384-400 |
| DOI | 10.31392/MFAT-npu26_4.2021.11 |
| MathSciNet |
MR4425717 |
| Milestones | Received 22/11/2020; Revised 14/04/2021 |
| Copyright | The 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
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},
}
