On the solvability of some systems of integro-differential equations with and without a drift

We prove the existence of solutions for some integro-differential systems containing equations with and without drift terms in the H2 spaces by virtue of the fixed point technique when the elliptic equations contain second order differential operators with and without Fredholm property, on the whole real line or on a finite interval with periodic boundary conditions. Let us emphasise that the study of the system case is more complicated than of the scalar situation and requires to overcome more cumbersome technicalities.