Bethe-Sommerfeld conjecture for periodic Schrödinger operators in strip (Q2320081)

This paper deals with the study of the Dirichlet Laplace operator in a straight planar strip perturbed by a bounded periodic symmetric operator. The main result of the paper under review gives a proof of the classical Bethe-Sommerfeld conjecture when the differential operator has finitely many gaps in its spectrum. In the final part of this paper, in the case of a sufficiently small period, the author establishes that the considered operator has no internal gaps in the spectrum. The conditions ensuring the absence of gaps are written as explicit inequalities.