@article{Gao2022, 
author = {Linkui Gao and Junyang Gao},
title = {Meromorphic solutions of        f          n        +      P          d        (  f  )  =      p          1            e                  α                  1                    z        +      p          2            e                  α                  2                    z        +      p          3            e                  α                  3                    z},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {10},
pages = {18297-18310},
keywords = {Nevanlinna theory, complex differential equations, exponential sums, meromorphic solutions},
url = {https://www.sciopen.com/article/10.3934/math.20221007},
doi = {10.3934/math.20221007},
abstract = {By using Nevanlinna of the value distribution of meromorphic functions, we investigate the transcendental meromorphic solutions of the non-linear differential equation         f          n        +      P          d        (  f  )  =      p          1            e                  α                  1                    z        +      p          2            e                  α                  2                    z        +      p          3            e                  α                  3                    z        ,where        P          d        (  f  ) is a differential polynomial in    f of degree    d  (  0  ≤  d  ≤  n  −  3  ) with small meromorphic coefficients and        p          i        ,      α          i        (  i  =  1  ,  2  ,  3  ) are nonzero constants. We show that the solutions of this type equation are exponential sums and they are in        Γ          0        ∪      Γ          1        ∪      Γ          3       which will be given in Section    1. Moreover, we give some examples to illustrate our results.}
}