Vitali Vougalter, Vitaly Volpert
Solvability in the sense of sequences for some non-Fredholm operators 
in higher dimensions
(178K, pdf)

ABSTRACT.  We study solvability of certain linear nonhomogeneous elliptic problems and establish that under reasonable technical assumptions the convergence in L^2(R^d) of their right sides implies the existence and the convergence 
in H^1(R^d) of the solutions. The equations involve the square roots of the sums of second order non-Fredholm differential operators and we rely on the methods of the spectral and scattering theory for Schrodinger type 
operators similarly to our earlier work [26].