Approximate controllability of second-order impulsive neutral stochastic differential equations with state-dependent delay and Poisson jumps

Abstract

Abstract We consider the approximate controllability for a class of second-order impulsive neutral stochastic differential equations with state-dependent delay and Poisson jumps in a real separable Hilbert space. Under the sufficient conditions, we obtain approximate controllability results by virtue of the theory of a strongly continuous cosine family of bounded linear operators combined with stochastic inequality technique and the Sadovskii fixed point theorem. Finally, we illustrate the main results by an example.

Keywords

• Approximate controllability
• Strongly continuous cosine family
• Second order
• Impulsive neutral stochastic differential equations
• State-dependent delay
• Poisson jumps