18-23 Vitali Vougalter, Vitaly Volpert

Solvability in the sense of sequences for some non-Fredholm operators in higher dimensions (178K, pdf) Feb 23, 18

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Abstract. We study solvability of certain linear nonhomogeneous elliptic problems and establish that under reasonable technical assumptions the convergence in L^2(R^d) of their right sides implies the existence and the convergence in H^1(R^d) of the solutions. The equations involve the square roots of the sums of second order non-Fredholm differential operators and we rely on the methods of the spectral and scattering theory for Schrodinger type operators similarly to our earlier work [26].

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