Existence of solutions and stability for impulsive neutral stochastic functional differential equations Mimia Benhadri a , Tom´ as Caraballo b , Halim Zeghdoudi c a Fr` eres Mentouri Constantine University, Department of Mathematics, Algeria. emails: mbenhadri@yahoo.com b Departamento de Ecuaciones Difererenciales y An´ alisis Num´ erico, Universidad de Sevilla c/ Tarfia s/n, 41012-Sevilla (Spain) email: caraball@us.es c LaPS Laboratory, Badji-Mokhtar University, Box 12, Annaba, 23000, Algeria. email: halim.zeghdoudi@univ-annaba.dz April 15, 2019 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 asymp- totic 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. Fi- nally, an example is exhibited to illustrate the effectiveness of the results. AMS Subject Classifications: 34K20, 34K13, 92B20 Keywords: Fixed points theory; Asymptotic stability in mean square; Neutral stochastic differential equations; Variable delays; Impulses. 1