Value distribution and uniqueness of difference polynomials and entire solutions of difference equations
Volume 102 / 2011
Annales Polonici Mathematici 102 (2011), 129-142
MSC: Primary 30D35; Secondary 39A05.
DOI: 10.4064/ap102-2-3
Abstract
This paper is devoted to value distribution and uniqueness problems for difference polynomials of entire functions such as $f^n(f-1)f(z+c)$. 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 $f^{n}+P(z)(\Delta _cf)^m=Q(z).$
