Messoud Efendiev, Vitali Vougalter
Solvability in the sense of sequences for some fourth order non-Fredholm operators
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ABSTRACT.  We study solvability of some linear nonhomogeneous elliptic problems and 
establish that under reasonable technical conditions the convergence in 
L^2(R^d) of their right sides implies the existence and the convergence in H^4(R^d) of the solutions. The problems contain the squares of the sums of second order non-Fredholm differential operators and we use the methods of the spectral and scattering theory for Schrodinger type operators analogously to our preceding work [28]. We especially emphasize that here we are dealing with the fourth order operators in contrast to the second order operators in [28].