Vitaly Volpert, Vitali Vougalter
Solvability conditions for some non Fredholm operators in a layer in four 
dimensions
(167K, pdf)

ABSTRACT.  We study solvability in H^2 of certain linear nonhomogeneous elliptic problems involving the sum of the periodic Laplacian and a Schroedinger operator without Fredholm property and prove that under reasonable technical conditions the convergence in L^2 of their right sides implies the existence and the convergence in H^2 of the solutions. 
We generalize the methods of spectral and scattering theory for 
Schroedinger type operators from our preceding work.