Existence and stability solutions of second-order partial neutral stochastic nonlinear differential systems with infinite delay (Q286371)

Summary: We consider a class of second-order neutral stochastic differential equations with infinite delay. First we establish a new set of sufficient conditions for the existence and uniqueness results for the system of equations which are discussed under non-Lipschitz with Lipschitz condition by the means of the successive approximation and theory of cosine families. Moreover, we give the continuous dependence of solutions on the initial data by means of corollary of the Bihari's inequality. Finally, an example is provided to illustrate our results.