摘要
In this paper, we consider the higher dimensional nonlinear beam equation:utt+△2u+σu + f(u)=0 with periodic boundary conditions, where the nonlinearity f(u) is a real-analytic function of the form f(u)=u3+ h.o.t near u=0 and σ is a positive constant. It is proved that for any fixed σ>0, the above equation admits a family of small-amplitude, linearly stable quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system.
In this paper, we consider the higher dimensional nonlinear beam equation: u tt + Δ2 u + σu + f(u) = 0 with periodic boundary conditions, where the nonlinearity f(u) is a real-analytic function of the form f(u) = u 3 + h.o.t near u = 0 and σ is a positive constant. It is proved that for any fixed σ > 0, the above equation admits a family of small-amplitude, linearly stable quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system.
基金
supported by National Natural Science Foundation of China (Grant Nos.10531050,10771098)
the Major State Basic Research Development of China and the Natural Science Foundation of Jiangsu Province(Grant No.BK2007134)
