TY - JOUR
T1 - On Reducibility of Beam Equation with Quasi-Periodic Forcing Potential
AU - Chang , Jing
JO - Communications in Mathematical Research 
VL - 4
SP - 289
EP - 302
PY - 2021
DA - 2021/05
SN - 32
DO - http://doi.org/10.13447/j.1674-5647.2016.04.01
UR - https://global-sci.org/intro/article_detail/cmr/18901.html
KW - beam equation, infinite dimension, Hamiltonian system, KAM theory,
reducibility.
AB - <p style="text-align: justify;">In this paper, the Dirichlet boundary value problems of the nonlinear
beam equation $u_{tt} + ∆^2u + αu + ϵϕ(t)(u + u^3
) = 0, α &gt; 0$ in the dimension one
is considered, where $u(t, x)$ and $ϕ(t$) are analytic quasi-periodic functions in $t$, and $ϵ$ is a small positive real-number parameter. It is proved that the above equation
admits a small-amplitude quasi-periodic solution. The proof is based on an infinite
dimensional KAM iteration procedure.</p>