摘要：In this paper, we study the solutions of the second-order generalized difference equation having the form of 1 Δ ℓ 2 u ( k ) + f ( k , u ( k ) ) = 0 , k ∈ [ a , ∞ ) , a > 0 , ℓ ∈ ( 0 , ∞ ) , where Δ ℓ u ( k ) = u ( k + ℓ ) − u ( k ) . Then we provide applications on ℓ 2 ( ℓ ) and c 0 ( ℓ ) . AMS Subject Classification:39A12, 39A70, 47B39, 39B60.
关键词：generalized difference equation ; generalized difference operator ; finite series and infinite series
