Weighted $S^p$-pseudo $S$-asymptotically periodic solutions for some systems of nonlinear delay integral equations with superlinear perturbation

This work is concerned with the existence of positive weighted pseudo $S$-asymptotically periodic solution in Stepanov-like sense for some systems of nonlinear delay integral equations. In this context, we will first be interested in establishing a suitable composition theorem, and then some existing results concerning the $S$-asymptotic periodicity in the scalar case are developed here for the vector case. We point out that, in this paper, we adopt some changes in the definitions, which, although slight, are necessary to accomplish the work.