## Abstract It is shown that there exist domains Ξ© β β^__N__^, which outside of some ball coincide with the strip β^__N__ β 1^ Γ (0, Ο) and for which the Dirichlet Laplacian β Ξ has eigenvalues within the subinterval (1, 4) of the essential spectrum (1, β).
Ramification of a multiple eigenvalue of the Dirichlet problem for the Laplacian under singular perturbation of the boundary condition
β Scribed by R. R. Gadyl'shin
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 1992
- Tongue
- English
- Weight
- 650 KB
- Volume
- 52
- Category
- Article
- ISSN
- 0001-4346
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract For certain unbounded domains the Laplace operator with Dirichlet condition is shown to have an unbounded sequence of eigenvalues which are embedded into the essential spectrum. A typical example of such a domain is a locally perturbed cylinder with circular crossβsection whose diameter
By using the Weinstein method, eigenvalues and eigenfunctions ofthe equation -zau = Au with Dirichlet boundary conditions are calculated for a certain class of regions. The regions are composed of unions of rectangles, and include L-shaped, single-notched and crossed rectangles. The method consists