We consider the spectral Dirichlet–Laplacian problem on a domain which is formed from a periodic waveguide Π perturbed by non-compact, non-periodic changes of geometry. We show that the domain perturbation causes an addition to the essential spectrum, which consists of isolated points belonging to the discrete spectrum of a model problem. This model problem is posed on a domain, which is just a compact perturbation of Π. We discuss the position of the new spectral components in relation to the essential spectrum of the problem in Π.

Original languageEnglish
Pages (from-to)922-933
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume463
Issue number2
DOIs
StatePublished - 15 Jul 2018

    Research areas

  • Dirichlet–Laplace problem, Essential spectrum, Non-periodic perturbation, Periodic, Sobolev space, Waveguide

    Scopus subject areas

  • Analysis
  • Applied Mathematics

ID: 35208430