Approximate controllability of stochastic nonlinear third-order dispersion equation

In this work, we consider a class of control systems governed by the stochastic nonlinear third-order dispersion equation in Hilbert spaces. We first prove the existence of mild solutions of stochastic nonlinear third-order dispersion equation by using fixed point theory, infinite dimensional semigroup properties, stochastic analysis techniques, and then a new set of sufficient conditions are formulated which guarantees the approximate controllability of the main problem. Finally, an example is provided to illustrate the application of the obtained results.Copyright (c) 2012 John Wiley & Sons, Ltd.