Bethe-Sommerfeld Conjecture

Abstract

We consider Schroedinger operator $-\Delta +V$ in $R^d$ ($d\ge 2$) with smooth periodic potential $V$ and prove that there are only finitely many gaps in its spectrum.

59 pages, 10 figures; to appear in Annales Henri Poincare

Cited by in corpus (1)

• Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential