Vitaly Volpert, Vitali Vougalter
Solvability in the sense of sequences for some non Fredholm operators with drift
(133K, pdf)

ABSTRACT.  We study solvability of certain linear nonhomogeneous elliptic equations 
and prove that under reasonable technical conditions the convergence in L^2 of their right sides yields the existence and the convergence in H^2 
of the solutions. The problems involve second order differential operators 
with or without Fredholm property, on the whole real line or on a finite interval with periodic boundary conditions. We show that the drift term involved in these equations provides the regularization for the solutions 
of our problems.