摘要：We prove the existence and uniqueness of a weighted pseudo asymptotically mild solution to the following class of abstract semilinear difference equations: u ( n + 1 ) = A ∑ k = − ∞ n a ( n − k ) u ( k + 1 ) + ∑ k = − ∞ n b ( n − k ) f ( k , u ( k ) ) , n ∈ Z , $$ u(n+1)= A \sum_{k=-\infty }^{n} a(n-k)u(k+1)+ \sum _{k=-\infty }^{n} b(n-k)f\bigl(k,u(k)\bigr),\quad n\in \mathbb{Z}, $$ where A is the generator of a resolvent sequence { S ( n ) } n ∈ N 0 $\{S(n)\}_{n\in \mathbb{N}_(}$ of bounded and linear operators defined in a Banach space X, the sequences a , b $a, b$ are complex-valued, and f ∈ l 1 ( Z × X , X ) $f\in l^)( \mathbb{Z}\times X, X)$ .
关键词：39A14;45D05;35B40;47D06;Weighted pseudo asymptotically mild solutions;Abstract difference equations;Resolvent sequences of operators
