摘要：In this paper, we investigate the second order self-adjoint discrete Hamiltonian system Δ [ p ( n ) Δ u ( n − 1 ) ] − L ( n ) u ( n ) + λ a ( n ) ∇ G ( u ( n ) ) + μ b ( n ) ∇ F ( u ( n ) ) = 0 $\Delta[p(n)\Delta u(n-1)]-L(n)u(n)+\lambda a(n)\nabla G(u(n))+\mu b(n)\nabla F(u(n))=0$ , where p , L : Z → R N × N $p,L:\mathbb{Z}\rightarrow\mathbb{R}^{N\times N}$ are both positive definite for all n ∈ Z $n\in\mathbb{Z}$ , and no symmetric condition on G and F is needed. We establish two new criteria to guarantee that the above system has at least two nontrivial homoclinic solutions or infinitely many homoclinic solutions via critical point theory.
关键词：homoclinic solutions ; discrete Hamiltonian systems ; critical point theory ; variational methods
