Heteroclinic orbits and heteroclinic chains for a discrete Hamiltonian system

@article{Zhang2010HeteroclinicOA,
  title={Heteroclinic orbits and heteroclinic chains for a discrete Hamiltonian system},
  author={H. J. Zhang and Zhixiang Li},
  journal={Science China Mathematics},
  year={2010},
  volume={53},
  pages={1555-1564}
}
In the present work we prove some existence results of heteroclinic orbits and heteroclinic chains for a second order discrete Hamiltonian system of the form Δ2q(t − 1) + V′(q(t)) = 0, t ∈ ℤ. The methods we use are variational in nature. Our results show that under general conditions, for each maximum point β of V, the above system possesses multiple heteroclinic orbits joining β and some other maximum points of V. We also prove that for any pair of distinct maximum points η and ξ of V, there… CONTINUE READING

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