Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps

Abstract

The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.

Keywords

• controllability
• impulsive neutral stochastic integro-differential equations
• Poisson jumps
• cosine functions of operators
• infinite delay
• Banach fixed point theorem