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. 
@article{MZM_2004_75_3_a3,
     author = {V. V. Grushin},
     title = {On the {Eigenvalues} of {Finitely} {Perturbed} {Laplace} {Operators} in {Infinite} {Cylindrical} {Domains}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {360--371},
     publisher = {mathdoc},
     volume = {75},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_3_a3/}
}
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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/