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

Abstract

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).

Entire Solutions Of Certain Non-Linear Differential-Difference Equations

“…In the above theorem, Rong and Xu [14] conjectured that case (iii) can be removed if N(r, 1/f ) = S(r, f ) for n = 2, 3.…”

“…Many researchers are working in this field, see [5,[10][11][12][13]17]. Recently Rong and Xu [14] studied a problem in this direction which is as follows:…”

On the meromorphic solutions of generalized q-difference equations

“…By the use of recent new difference versions of Nevanlinna theory, many studies [1,5,[11][12][13][14][15][16][17][18][19][20] of the properties of meromorphic solutions of the difference equation…”

Exponential Polynomials and Nonlinear Differential-Difference Equations

“…Many papers recently have focused on solvability and existence of solutions of nonlinear differential-difference equations, see [5][6][7][8][9][10][11][12][13][14][15][16].…”