Uniform asyptotic formulae for eigenfunctions of Sturm--Liouville   operators with singular potentials
  In this paper we study a Sturm--Liouville operator $Ly=-y''+q(x)y$ in the space $L_2[0,\pi]$ with Direchlet boundary conditions. Here the potential $q$ is a fitst order distribution $q\in W_2^{-1}[0,\pi]$. Such operators were defined in our previous papers. Here we study an asymptotic behaviour of eigenfunctions with uniform estimates of rests. We obtain this estimates also for potentials from Sobolev spaces $q\in W_2^{\theta-1}$, where $\theta\in[0,1/2)$. 
A. M. Savchuk