The Banach Spaces and with Application to the Approximate Controllability of Stochastic Partial Functional Differential Equations with Infinite Delay

Abstract

In this article, we shall consider the approximate controllability for stochastic partial functional differential equations with infinite delay in space (p > 2). By using the Banach fixed point theorem, we obtain the sufficient conditions. At the same time, we shall present an example for Volterra stochastic integro-differential reaction–diffusion equation which illustrates our main theorem.

Keywords:

• Approximate controllability
• Banach fixed point theorem
• Infinite delay
• Stochastic partial functional differential equations

Acknowledgments

Supported by the NNSF of China.