Growth and zeros of meromorphic solution of some linear difference equations

In this paper, we study growth and zeros of linear difference equations P n ( z ) f ( z + n ) + ⋯ + P 1 ( z ) f ( z + 1 ) + P 0 ( z ) f ( z ) = F ( z ) where F ( z ) , P n ( z ) , … , P 0 ( z ) are polynomials with F P n P 0 ≢ 0 and satisfy deg ( P n + ⋯ + P 0 ) = max { deg P j : j = 0 , … , n } ⩾ 1 . The corresponding homogeneous equation of the above equation is also investigated.