Existence of solutions and stability for impulsive neutral stochastic functional differential equations

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.

Keywords:

• Fixed points theory
• asymptotic stability in mean square
• neutral stochastic differential equations
• variable delays
• impulses

AMS Subject Classifications:

• 34K20
• 34K13
• 92B20

Additional information

Funding

The research of the second author has been partially supported by grant MTM2015-63723-P (MINECO/FEDER, EU), and Junta de Andalucía (Spain) under the Proyecto de Excelencia P12-FQM-1492. Also, this work was funded by European Mathematical Society.