Solvability conditions for some non-Fredholm operators

Source abstract

Abstract 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 paper concerns solvability conditions for the equation –Δ u + V ( x ) u – au = f where a ≥ 0. The conditions are formulated in terms of orthogonality of the function f to the solutions of the homogeneous adjoint equation.