A note on the neutral stochastic functional differential equation with infinite delay and Poisson jumps in an abstract space

Abstract

In this note, we prove the existence and uniqueness of the solution to neutral stochastic functional differential equation with infinite delay and Poisson jumps in the phase space B with non-Lipschitz coefficients. The known results that appeared in the studies by Ren and Xia [Appl. Math. Comput. 210, 72 (2009); Ren and XiaAppl. Math. Comput. 214, 457 (2009)] and Xu and Hu [Acta Appl. Math. (unpublished)] are generalized and improved. An example is provided to illustrate the theory.