摘要
In this paper, we consider the lattice SchrSdinger equations iqn（t） = tan π（na＋x）qn（t） ＋ε（qn＋1（t） ＋ qn-1（t）） ＋δVn（t）｜qn（t）｜2τ-2qn（t）,with a satisfying a certain Diophantine condition, x∈ R/Z, and t- = 1 or 2, where vn（t） is a spatial localized real bounded potential satisfying ｜vn（t）｜ Ce-plnl. We prove that the growth of H1 norm of the solution {qn（t）}n∈Z is at most logarithmic if the initial data {qn（0）}n∈Z ∈ H1 for e sufficiently small and a.e. x fixed. Furthermore, suppose that the linear equation has a time quasi-periodic potential, i.e.,
In this paper, we consider the lattice SchrSdinger equations iqn（t） = tan π（na＋x）qn（t） ＋ε（qn＋1（t） ＋ qn-1（t）） ＋δVn（t）｜qn（t）｜2τ-2qn（t）,with a satisfying a certain Diophantine condition, x∈ R/Z, and t- = 1 or 2, where vn（t） is a spatial localized real bounded potential satisfying ｜vn（t）｜ Ce-plnl. We prove that the growth of H1 norm of the solution {qn（t）}n∈Z is at most logarithmic if the initial data {qn（0）}n∈Z ∈ H1 for e sufficiently small and a.e. x fixed. Furthermore, suppose that the linear equation has a time quasi-periodic potential, i.e.,
