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Theoretical and Mathematical Physics

, Volume 195, Issue 2, pp 690–703 | Cite as

Absence of Gaps in a Lower Part of the Spectrum of a Laplacian with Frequent Alternation of Boundary Conditions in a Strip

  • D. I. BorisovEmail author
Article
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Abstract

We consider the Laplacian in a planar infinite straight strip with frequent alternation of boundary conditions. We show that for a sufficiently small alternation period, there are no gaps in a lower part of the spectrum. In terms of certain numbers and functions, we write an explicit upper bound for the period and an expression for the length of the lower part of the spectrum in which the absence of gaps is guaranteed.

Keywords

Bethe–Sommerfeld conjecture gap periodic operator alternation of boundary conditions Laplacian infinite strip 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Institute of Mathematics with Computing CentreUfa Science CenterRAS, UfaRussia
  2. 2.Akhmulla Bashkir State Pedagogical UniversityUfaRussia
  3. 3.University of Hradec KrálovéHradec KrálovéCzech Republic

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