Existence of solutions and stability for impulsive neutral stochastic functional differential equations. Issue 5 (3rd September 2019)

• Record Type: Journal Article
• Authors: Benhadri, Mimia; Caraballo, Tomás; Halim, Zeghdoudi
• Is Part Of: Stochastic analysis and applications. Volume 37:Issue 5(2019)
• Page Start: 777
• Page End: 798
• Publication Date: 2019-09-03
• Subjects: Fixed points theory -- asymptotic stability in mean square -- neutral stochastic differential equations -- variable delays -- impulses; 34K20 -- 34K13 -- 92B20; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2019.1611449
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: In this paper, we prove some results on the existence of solutions and the mean square asymptotic stability for a class of impulsive neutral stochastic differential systems with variable delays by using a contraction mapping principle. Namely, a sufficient condition ensuring the asymptotic stability is proved. The assumptions do not impose any restrictions neither on boundedness nor on the differentiability of the delay functions. In particular, the results improve some previous ones in the literature. Finally, an example is exhibited to illustrate the effectiveness of the results.