Quasi-periodically forced and reversible vibrations of beam equations with Liouvillean frequencies.

The present paper is concerned with the existence of response solutions of quasi-periodic type for a class of quasi-periodically forced, non-Hamiltonian but reversible nonlinear beam equations. We do not suppose the basic frequency ω ∈ R 2 of the forcing term is Diophantine or Brjuno, and it might be Liouvillean, which is weaker than the Diophantine or Brjuno frequency. The proof is based on an improved Kolmogorov–Arnold–Moser (KAM) theorem for infinite-dimensional reversible systems with non-reducible normal form. [ABSTRACT FROM AUTHOR]