Solvability conditions for some non-Fredholm operators
Résumé
We obtain solvability conditions for some elliptic equations involving non Fredholm operators with the methods of spectral theory and scattering theory for Schrödinger type operators. One of the main results of the work concerns solvability conditions for the equation −Delta u+V (x)u−au = f where a ≥ 0. They are formulated in terms of orthogonality of the function f to the solutions of the homogeneous adjoint equation.
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