摘要：In this paper, we investigate the nontrivial solutions to the difference equations − Δ 2 u ( k − 1 ) = f ( k , u ( k ) ) for all k ∈ Z [ 0 , T ] and subject to u ( 0 ) = 0 = Δ u ( T ) , and establish the existence results of a nontrivial solution under some resonant conditions.
关键词：discrete boundary value problem ; resonance ; critical group
