Geodesic
The problem of steady-state oscillations of a~transversally isotropic half-cylinder
Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 579-602

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The authors study the problem of solvability on the semiaxis of the equation $$ \mathscr P(u)=-A\frac{d^2u}{dy^2}+iB\frac{du}{dy}+(C-\omega^2R)u=0, $$ where $\omega\in\mathbf R$, and $A$, $B$, $C$, and $R$ are unbounded symmetric operators in a Hilbert space $\mathfrak H$. Models of this equation are problems of steady-state oscillations of an elastic half-cylinder with various boundary conditions. The main results are theorems on factorization of a pencil related to this problem and solvability theorems. 
@article{SM_1992_73_2_a17,
     author = {A. A. Shkalikov and A. V. Shkred},
     title = {The problem of steady-state oscillations of a~transversally isotropic half-cylinder},
     journal = {Sbornik. Mathematics},
     pages = {579--602},
     publisher = {mathdoc},
     volume = {73},
     number = {2},
     year = {1992},
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     url = {http://geodesic.mathdoc.fr/item/SM_1992_73_2_a17/}
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A. A. Shkalikov; A. V. Shkred. The problem of steady-state oscillations of a~transversally isotropic half-cylinder. Sbornik. Mathematics, Tome 73 (1992) no. 2, pp. 579-602. http://geodesic.mathdoc.fr/item/SM_1992_73_2_a17/