On regular and singular perturbations of acoustic and quantum waveguides

Abstract

We consider regular and singular perturbations of the Dirichlet and Neumann boundary value problems for the Helmholtz equation in $n$-dimensional cylinders. Existence of eigenvalues and their asymptotics are studied.

References in corpus (2)

• Bound states in weakly deformed strips and layers
• On local perturbations of Shrodinger operator in axis

Cited by in corpus (9)

• On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition
• Homogenization of the planar waveguide with frequently alternating boundary conditions
• Spectrum of the Magnetic Schrodinger Operator in a Waveguide with Combined Boundary Conditions
• Non-Hermitian spectral effects in a PT-symmetric waveguide
• Planar waveguide with "twisted" boundary conditions: discrete spectrum
• Discrete spectrum of a pair of nonsymmetric waveguides coupled by a window
• Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations
• A quantum waveguide with Aharonov Bohm magnetic field
• Spectral asymptotics for eigenvalues and resonances in the presence of a change of boundary conditions