Vitali Vougalter
Solvability in the sense of sequences for some non-Fredholm operators related to the double scale anomalous diffusion
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ABSTRACT. We address the solvability of certain linear nonhomogeneous elliptic equations and establish that under reasonable technical assumptions the
convergence in L^2(R^d) of their right sides yields the existence and the convergence in H^{2s}(R^d) of the solutions. In the first part of the article the problem contains the sum of the two negative Laplacians raised to two distinct fractional powers. In the second part we generalize the results obtained by incorporating a shallow, short-range potential into the equation and we use the methods of the spectral and scattering theory for the non-Fredholm Schrodinger type operators.