Geodesic
On eigenvalues of a~$\mathscr{P\!T}$-symmetric operator in a~thin layer
Sbornik. Mathematics, Tome 208 (2017) no. 2, pp. 173-199

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We consider an elliptic operator with variable coefficients in a thin three-dimensional layer with $\mathscr{P\!T}$-symmetric boundary conditions. We study the effect of the appearance of isolated eigenvalues at the edges of the gaps in the essential spectrum. We obtain sufficient conditions that guarantee that such eigenvalues either exist or are absent near a given edge of a gap. In the case of existence, the first terms in the asymptotic expansion of these emerging eigenvalues are calculated. Bibliography: 34 titles.
Keywords: thin domain, $\mathscr{P\!T}$-symmetric operator, edge of a gap, asymptotics, periodic operator. 
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     author = {D. I. Borisov and M. Znojil},
     title = {On eigenvalues of a~$\mathscr{P\!T}$-symmetric operator in a~thin layer},
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D. I. Borisov; M. Znojil. On eigenvalues of a~$\mathscr{P\!T}$-symmetric operator in a~thin layer. Sbornik. Mathematics, Tome 208 (2017) no. 2, pp. 173-199. http://geodesic.mathdoc.fr/item/SM_2017_208_2_a0/