Geodesic
On spectral properties of one boundary value problem with a surface energy dissipation
Ufa mathematical journal, Tome 9 (2017) no. 2, pp. 3-16

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We study a spectral problem in a bounded domain ${\Omega \subset \mathbb{R}^{m}}$, depending on a bounded operator coefficient $Q>0$ and a dissipation parameter $\alpha>0$. In the general case we establish sufficient conditions ensuring that the problem has a discrete spectrum consisting of countably many isolated eigenvalues of finite multiplicity accumulating at infinity. We also establish the conditions, under which the system of root elements contains an Abel-Lidskii basis in the space $ L_2(\Omega)$. In model one- and two-dimensional problems we establish the localization of the eigenvalues and find critical values of $\alpha$.
Keywords: spectral parameter, quadratic operator pencil, localization of eigenvalues, compact operator, Schatten-von-Neumann classes $S_p$, Abel-Lidskii basis property. 
@article{UFA_2017_9_2_a0,
     author = {O. A. Andronova and V. I. Voytitskiy},
     title = {On spectral properties of one boundary value problem with a surface energy dissipation},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2017_9_2_a0/}
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O. A. Andronova; V. I. Voytitskiy. On spectral properties of one boundary value problem with a surface energy dissipation. Ufa mathematical journal, Tome 9 (2017) no. 2, pp. 3-16. http://geodesic.mathdoc.fr/item/UFA_2017_9_2_a0/