Solvability in the sense of sequences for some non Fredholm operators related to the superdiffusion

We study solvability of some linear nonhomogeneous elliptic equations and show that under reasonable technical conditions the convergence in L²(R^d) of their right sides yields the existence and the convergence in H¹(R^d) of the solutions. The problems involve the square roots of the second order non Fredholm differential operators and we use the methods of spectral and scattering theory for Schrödinger type operators similarly to our preceding work (Volpert and Vougalter in Electron J Differ Equ 160:16, 2013).