Vitali Vougalter
Solvability in the sense of sequences for some non-Fredholm operators 
with the drift and bi-Laplacian
(137K, pdf)

ABSTRACT.  We study the solvability of some linear nonhomogeneous elliptic equations 
and establish that under certain technical conditions the convergence in 
L^2 of their right sides yields the existence and the convergence in H^4 
of the solutions. The problems involve the fourth order differential operators with or without the Fredholm property, particularly the fourth derivative operator, on the whole real line or on a finite interval with 
periodic boundary conditions. We demonstrate that the transport term contained in these equations provides the regularization of the solutions.