摘要：In this article, we discuss how to use a standard minimizing argument in critical point theory to study the existence of non-trivial homoclinic solutions of the following second-order non-autonomous discrete systems Δ 2 x n - 1 + A Δ x n - L ( n ) x n + ∇ W ( n , x n ) = 0 , n ∈ Z , without any periodicity assumptions. Adopting some reasonable assumptions for A and L, we establish that two new criterions for guaranteeing above systems have one non-trivial homoclinic solution. Besides that, in some particular case, for the first time the uniqueness of homoclinic solutions is also obtained. MSC: 39A11.
关键词：homoclinic solution ; variational functional ; critical point ; subquadratic second-order discrete system
