Geodesic
On the accumulation of eigenvalues of operator pencils connected with the problem of vibrations in a~viscoelastic rod
Matematičeskie zametki, Tome 79 (2006) no. 3, pp. 369-383

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In this paper, we study the problem of the boundary accumulation of a discrete spectrum, which is essential for a boundary-value problem of fourth order arising in the theory of small transverse vibrations in an inhomogeneous viscoelastic rod (a Kelvin–Voigt body). We establish conditions for such an accumulation and its asymptotics, which are expressed in terms of the coefficients defining the problem posed by the differential expression. The results obtained are illustrated by numerical computation data. 
@article{MZM_2006_79_3_a4,
     author = {A. A. Vladimirov},
     title = {On the accumulation of eigenvalues of operator pencils connected with the problem of vibrations in a~viscoelastic rod},
     journal = {Matemati\v{c}eskie zametki},
     pages = {369--383},
     publisher = {mathdoc},
     volume = {79},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_3_a4/}
}
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A. A. Vladimirov. On the accumulation of eigenvalues of operator pencils connected with the problem of vibrations in a~viscoelastic rod. Matematičeskie zametki, Tome 79 (2006) no. 3, pp. 369-383. http://geodesic.mathdoc.fr/item/MZM_2006_79_3_a4/