This article is cited in 12 papers

The problem of steady-state oscillations of a transversally isotropic half-cylinder

A. A. Shkalikov, A. V. Shkred


Abstract: 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.

UDC: 517.43

MSC: Primary 73D30; Secondary 35J25

Received: 16.04.1990

 English version: Mathematics of the USSR-Sbornik, 1992, 73:2, 579–602

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