Existence, uniqueness, and stability of mild solutions for second-order neutral stochastic evolution equations with infinite delay and Poisson jumps

In this paper, we study a class of second-order neutral stochastic evolution equations with infinite delay and Poisson jumps (SNSEEIPs), in which the initial value belongs to the abstract space B. We establish the existence and uniqueness of mild solutions for SNSEEIPs under non-Lipschitz condition with Lipschitz condition being considered as a special case by means of the successive approximation. Furthermore, we give the continuous dependence of solutions on the initial data by means of a corollary of the Bihari inequality. An application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given to illustrate the theory. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4739406]