20-54 Messoud Efendiev, Vitali Vougalter

Solvability in the sense of sequences for some fourth order non-Fredholm operators (209K, pdf) Jul 10, 20

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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. We especially emphasize that we deal with the fourth order operators in contrast to the second order operators in [29] and investigate the dependence of the solvability conditions on the dimension of our problem when the constant a=0. We also consider the case of solvability with a single potential in an arbitrary dimension.

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