Vitali Vougalter, Vitaly Volpert
On the solvability in the sense of sequences for some non Fredholm operators related to the anomalous diffusion
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ABSTRACT. We study solvability of some linear nonhomogeneous elliptic problems
and prove that under reasonable technical conditions the convergence
in L^2(R^d) of their right sides implies the existence and the convergence
in H^2s (R^d) of the solutions. The equations involve the second order
non Fredholm differential operators raised to certain fractional powers
s and we use the methods of spectral and scattering theory for Schrodinger type operators developed in our preceding work [26].