Examples of embedded eigenvalues for the Dirichlet‐Laplacian in domains with infinite boundaries
- 1 February 1990
- journal article
- research article
- Published by Wiley in Mathematical Methods in the Applied Sciences
- Vol. 12 (2) , 177-182
- https://doi.org/10.1002/mma.1670120208
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 cross‐section whose diameter in some bounded subset is greater than at infinity.Keywords
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