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Value distribution and uniqueness of difference polynomials and entire solutions of difference equations

Xiaoguang Qi (2011)

Annales Polonici Mathematici

This paper is devoted to value distribution and uniqueness problems for difference polynomials of entire functions such as fⁿ(f-1)f(z+c). We also consider sharing value problems for f(z) and its shifts f(z+c), and improve some recent results of Heittokangas et al. [J. Math. Anal. Appl. 355 (2009), 352-363]. Finally, we obtain some results on the existence of entire solutions of a difference equation of the form f + P ( z ) ( Δ c f ) m = Q ( z ) .

Value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations

Li-Qin Luo, Xiu-Min Zheng (2016)

Open Mathematics

In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.

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