Solvability of some integro-differential equations with drift (Q2176806)

The authors consider the integro-differential equation \[\frac {d^2u}{dx^2}+ b\frac{du}{dx}+ au+ \int_\Omega G(x- y)F(y,u(y))\,dy= 0.\] Imposing a series of technical conditions on the data, they prove existence and uniqueness of solutions of this equation by means of the Banach-Caccioppoli fixed point theorem.