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 .
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