volume 170, issue 2, P359-373 1995
DOI: 10.1007/bf02108333
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Abstract: We study the spectral theory of the fourth-order eigenvalue problemwhere the functions a and p are periodic and strictly positive. This equation models the transverse vibrations of a thin straight (periodic) beam whose physical characteristics are described by a and p.We examine the structure of the spectrum establishing the fact that the periodic and antiperiodic eigenvalues are the endpoints of the spectral bands. We also introduce an entire function, which we denote by E(λ), connected to the spectral theory…

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