Geodesic
On the Eigenvalues of Finitely Perturbed Laplace Operators in Infinite Cylindrical Domains
Matematičeskie zametki, Tome 75 (2004) no. 3, pp. 360-371.

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In this paper, sufficient conditions for the existence of eigenvalues of a finitely perturbed Laplace operator in an infinite cylindrical domain and their asymptotics in the small parameter are given. Similar questions for tubes, i.e., deformed cylinders, are also considered. 
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V. V. Grushin. On the Eigenvalues of Finitely Perturbed Laplace Operators in Infinite Cylindrical Domains. Matematičeskie zametki, Tome 75 (2004) no. 3, pp. 360-371. http://geodesic.mathdoc.fr/item/MZM_2004_75_3_a3/

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