Meromorphic solutions of difference Painlevé IV equations

摘要

In this paper, we investigate the family of difference Painlevé IV equation ( w ( z + 1 ) + w ( z ) ) ( w ( z ) + w ( z − 1 ) ) = R ( z , w ) , where R is rational in w and meromorphic in z. If the equation assumes an admissible meromorphic solution of hyper-order ρ 2 ( w ) 1 , we fix the degree of R ( z , w ) , and we give some further discussions. MSC:39A10.