As we know we can not multiply distribution
does it mean that there are no weak distributional solution to non linear differntial equation ??
for example $ xy'(x) ==$ has the solution $ y(x)= CH(x)$ for the heaviside step function
however if there is a term of the form $ y(x)y'(x) $ and you try for your nonllinear ode the solution distribution $ y(X)=h(x) $
you should handel with $ H(x)\delta (x) $ or this could be enven worse for example $ \delta(x) \delta ' (x) $
sop what happens with weaks solutions for nonlinear ODE ?