Successive approximation of neutral stochastic partial integrodifferential equations with infinite delay and Poisson jumps

Abstract

This work presents the result on existence, uniqueness of mild solutions of neutral stochastic partial integro-differential equations with infinite delay and Poisson jumps in real separable Hilbert spaces, We study the continous dependence of solution on the initial value. The nonlinear term in our equations are not assumed to Lipschitz continous. To obtain the results, we use the theory of resolvent operator devolopped in R. Grimmer (1982) and by using the method of successive approximation under sufficient condition.