Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 160, pp. 1-16.

Title: Solvability in the sense of sequences to some non-Fredholm operators
        
Authors: Vitaly Volpert   (Univ. Lyon 1, Villeurbanne, France)
         Vitali Vougalter (Univ. of Cape Town, Rondebosch, South Africa)

Abstract:
 We study the solvability of certain linear nonhomogeneous
 elliptic problems and show that under reasonable technical conditions the
 convergence in $L^2(\mathbb{R}^d)$ of their right sides implies the
 existence and the convergence in $H^2(\mathbb{R}^d)$ of the solutions. The
 equations involve second order differential operators without Fredholm
 property and we use the methods of spectral and scattering theory for
 Schrodinger type operators analogously to our preceding work [17].

Submitted March 8, 2013. Published July 12, 2013.
Math Subject Classifications: 35J10, 35P10, 47F05
Key Words: Solvability conditions; non Fredholm operators; Sobolev spaces.