Periodic solutions of abstract differential equations: the Fourier method
The operator , , , is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types and , respectively.
It is proved that any weak solution to a nonlinear beam equation is eventually globally oscillatory, i.e., there is a uniform oscillatory interval for large times.
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