Recent Developments in the Theory of the Periodic Euler-Bernoulli Equation

Vassilis Papanicolaou National Technical University of Athens (NTUA)

We develop the theory of the periodic Euler-Bernoulli equation following the spirit of the theory of Hill’s equation. We establish the equality of algebraic and geometric multiplicities at the endpoints of the gaps and pseudogaps. We also propose an Euler-Bernoulli analog of the Hill’s Dirichlet spectrum by considering a multipoint boundary value problem.