Vitali Vougalter
On the solvability in the sense of sequences for some non-Fredholm operators in higher dimensions
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ABSTRACT.  We study solvability of some linear nonhomogeneous elliptic equations and establish that under reasonable technical conditions the convergence in L^2(R^d) of their right sides yields the existence and the convergence in L^2(R^d) of the solutions. The problems contain the fractional powers of the sums of second order non-Fredholm differential operators and we use the methods of the spectral and scattering theory for Schrodinger type oprators analogously to our preceding article [27].