Abstract
In this paper, we mainly investigate properties on solution sets of a semi-linear stochastic evolution integro-differential inclusion with Poisson jumps and non-local initial conditions. We firstly establish the existence of solutions to the addressed equation via weak topology technique. Through establishing the estimate on noncompactness measure of integrals for Poisson jumps, we further show that the solution set is a compact -set when the resolvent operator is compact or non-compact, respectively.
Acknowledgements
Authors would like to thank the anonymous referee and the associate editor for carefully reading this manuscript and giving valuable comments to improve the previous version of this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).