On the solvability of some systems of integro-differential equations with concentrated sources

The article is devoted to the existence of solutions of a system of integro-differential equations in the case of the normal diffusion and the influx/efflux terms proportional to the Dirac delta function. The proof of the existence of solutions relies on a fixed point technique. We use the solvability conditions for the non-Fredholm elliptic operators in unbounded domains.