On the Entire Solutions of a Certain Class of Nonlinear Differential Equations

摘要

By using the fundamental theorems of Nevanlinna theory for meromorphic functions, one can determine whether the following type of nonlinear differential equation P sub n (Z) (f sup n) (Z) + P sub (n-1) (Z) f sup (n-1) (Z) + ... + P sub 1 (Z) f (Z) + P sub 0 (Z) + f1 (Z) = Q sub 1 (Z)(e to the power mp(Z)) + Q sub 2 (Z)(e to the power kp(Z)), has entire solutions or not, where p(z), (P sub i)(Z) (i = 0, 1, 2, ... n) and (Q sub j)(Z) (j = 1, 2) are polynomials, and m and k are integers. (Author)