Geodesic
Multiplicity of eigenvalues in certain boundary value problems for the Helmholtz equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 783-791

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Boundary value problems for two-layer cylindrical waveguides (namely, for a circular two-layer closed waveguide and a dielectric waveguide in an unbounded medium) are considered. It is shown that the same eigenvalues determining the wave numbers of waves in the waveguides can correspond to different solutions of the boundary value problem. 
@article{ZVMMF_2013_53_5_a8,
     author = {V. A. Malakhov and A. V. Nazarov and A. S. Raevskii and S. B. Raevskii},
     title = {Multiplicity of eigenvalues in certain boundary value problems for the {Helmholtz} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {783--791},
     publisher = {mathdoc},
     volume = {53},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_5_a8/}
}
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V. A. Malakhov; A. V. Nazarov; A. S. Raevskii; S. B. Raevskii. Multiplicity of eigenvalues in certain boundary value problems for the Helmholtz equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 783-791. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_5_a8/