Entire solutions of certain type of differential equations

Abstract

By utilizing Nevanlinna's value distribution theory of meromorphic functions, we solve the transcendental entire solutions of the following type of nonlinear differential equations in the complex plane: f n ( z ) + P ( f ) = p 1 e α 1 z + p 2 e α 2 z , where p 1 and p 2 are two small functions of e z , and α 1 , α 2 are two nonzero constants with some additional conditions, and P ( f ) denotes a differential polynomial in f and its derivatives (with small functions of f as the coefficients) of degree no greater than n − 1 .