Solvability in the sense of sequences to some non-Fredholm operators
Résumé
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 [