Solvability Conditions For Some Non Fredholm Operators in a Layer in Four Dimensions - Volpert, Vitaly; Vougalter, Vitali (Discontinuity, Nonlinearity, and Complexity, 2026)
We study solvability in H2 of certain linear nonhomogeneous elliptic prob- lems involving the sum of the periodic Laplacian and a Schrödinger oper- ator without Fredholm property and prove that under reasonable technical conditions the convergence in L2 of their right sides implies the existence and the convergence in H2 of the solutions. We generalize the methods of spectral and scattering theory for Schro ̈dinger type operators from our preceding work [1].