Existence results of mild solutions for some stochastic integrodifferential equations with state-dependent delay and noninstantaneous impulses in Hilbert spaces. Issue 1 (31st December 2022)

• Record Type: Journal Article
• Authors: Niang, Mamadou; Diop, Amadou; Didiya, Mohamed; Diop, Mamadou Abdoul
• Editors: Hemen, Dutta
• Is Part Of: Research in Mathematics. Volume 9:Issue 1(2022)
• Publication Date: 2022-12-31
• Subjects: Wiener process -- resolvent operator -- stochastic evolution equations -- hausdorff measure of noncompactness -- state dependent delay -- impulsive effects
• DOI: 10.1080/27684830.2022.2141173
• Languages: English
• ISSNs: 2768-4830

Abstract

ABSTRACT: The primary objective of this work is to investigate the existence of mild solutions for some neutral stochastic integrodifferential systems in Hilbert spaces. These systems have a state-dependent delay and noninstantaneous impulses. In order to achieve this objective, the neutral stochastic integrodifferential system that has been proposed with state-dependent delay and noninstantaneous impulses is converted into an equivalent fixed point problem by means of an appropriate integral operator.Together with the theory of stochastic analysis, we develop several existence results that are founded on the theory of resolvent operators in the sense of Grimmer, Hausdorff's measures of noncompactness, and fixed point theorems.In the last part of this paper, specific examples are used to show how the general conclusions reached in this paper are made.