Start with a system of three equations such that two of the equations are ordinary or partial differential equations, but one of them is an integral equation as follows:
$C = \int_{0}^{\infty} X \: dt$,
where $X$ is some product of $A$ and $B$, $A$ being determined by the first differential equation and $B$ being determined by the second one.
Since the integral equation is non-local, is it conceivable that there could be some of type of theory which allow one to determine existence of solutions to this system of equations? If one can convert the integral equation to a functional-differential equation, is there an existence theory in this case or does it depend on the specific details of the two differential equations?
