Existence and controllability results for second-order neutral
stochastic equations with non-Lipschitz coefficient driven by Rosenblatt
process
Abstract
In this paper we consider a class of second-order impulsive stochastic
functional differential equations driven simultaneously by a Rosenblatt
process and 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.\end{abstract}