A class of stochastic nonlocal evolution equations with nonlocal initial conditions

In this paper, we consider the existence and uniqueness of mild solutions for stochastic nonlocal evolution equations with Lévy diffusion operator and nonlocal initial conditions. Based on the continuity of the Lévy semigroup and the technique of the measure of noncompactness, we establish the local existence of mild solutions in [Formula: see text] under some weaker growth conditions. Moreover, we obtain the existence of mild solutions on any finite interval by using the general growth conditions on the nonlinear. Finally, the global existence and uniqueness of mild solutions follow from the additional Lipschitz conditions on nonlinear terms.