Successive Approximation of Neutral Stochastic Partial Integrodifferential Systems with State-Dependent Delay and Poisson Jumps

This study establishes the existence and uniqueness of moderate solutions (MD) of stochastic neutral partial integrodifferential (SNPID) systems with state-dependent delay and Poisson jumps (PJ). We look into the solution’s ongoing dependence on the initial point. Our equations’ nonlinear component is not considered to obey Lipschitz criteria. We begin by presenting the outcomes of the successive approximation and the developed resolvent operator (Grimmer, Trans. Am. Math. Soc. 273(1):333–349, 1982)