Asymptotic Relation as Boundary Condition

I want to solve a system of non-linear second order differential equations. For some of the unknown functions there are boundary conditions that i know how to write them in Mathematica. One of the unknows satisfies the following asymptotic expression:

$$b(r rightarrow infty) sim frac{r^2}{l^2} $$

My question is if is there a way to use an asymptotic relation as a boundary condition in Mathematica.