Differential equations with coeffcients in Sobolev spaces

I would like to talk about ordinary and delay differential equations with coefficients in Sobolev spaces. An example of a differential system with measurable singular right hand side is the system of motion of n-bodies.
When we deal with nonsmooth differential equations, then some obstacles appear: for instance the superposition f(t,y(t)) does not have to be measurable.
A candidate for a solution of such problem is the concept of the trace operator defining the trace on a graph on a curve.