Three Results on the Nonlinear Differential Equations and Differential-Difference Equations

We mainly study the transcendental entire solutions of the differential equation f n ( z ) + P ( f ) = p 1 e α 1 z + p 2 e α 2 z , where p 1 , p 2 , α 1 and α 2 are nonzero constants satisfying α 1 ≠ α 2 and P ( f ) is a differential polynomial in f of degree n − 1 . We improve Chen and Gao’s results and partially answer a question proposed by Li (J. Math. Anal. Appl. 375 (2011), pp. 310–319).

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