Solvability in the sense of sequences for some logarithmic Schrödinger operators in higher dimensions

We study the solvability of certain linear nonhomogeneous equations containing the logarithm of the sum of the two Schrödinger operators in higher dimensions and demonstrate that under the reasonable technical assumptions the convergence in L(R) of the right sides yields the existence and the convergence in L(R) of the solutions. The equations involve the operators without the Fredholm property and we use the methods of the spectral and scattering theory for the Schrödinger type operators to generalize the results of our preceding work Efendiev and Vougalter(Monatsh. Math., 2023). As distinct from the many previous articles on the subject, for the operators contained in our equations the essential spectra fill the whole real line.