# The periodic Euler-Bernoulli equation

@article{Papanicolaou2003ThePE,
title={The periodic Euler-Bernoulli equation},
author={Vassilis G. Papanicolaou},
journal={Transactions of the American Mathematical Society},
year={2003},
volume={355},
pages={3727-3759}
}
• V. Papanicolaou
• Published 29 May 2003
• Mathematics
• Transactions of the American Mathematical Society
We continue the study of the Floquet (spectral) theory of the beam equation, namely the fourth-order eigenvalue problem [a(x)u(x)] = λρ(x)u(x), -∞ < x < ∞, where 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. Here we develop a theory analogous to the theory of the Hill operator -(d/dx) 2 + q(x). We first review some facts and notions from our…
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