## Abstract and Applied Analysis

### Some Properties on Complex Functional Difference Equations

#### Abstract

We obtain some results on the transcendental meromorphic solutions of complex functional difference equations of the form $\sum \lambda \in I{\alpha }_{\lambda }(z)({\prod }_{j=0}^{n}f{(z+{c}_{j})}^{{\lambda }_{j}})=R(z,f\circ p)=(({a}_{0}(z)+{a}_{1}(z)(f\circ p)+ \cdots +{a}_{s}(z)$$(f\circ p{)}^{s})/({b}_{0}(z)+{b}_{1}(z)(f\circ p)+ \cdots +{b}_{t}(z)(f\circ p{)}^{t}))$, where $I$ is a finite set of multi-indexes $\lambda =({\lambda }_{\mathrm{0}},{\lambda }_{\mathrm{1}},\dots ,{\lambda }_{n})$, ${c}_{0}=0,{c}_{j}\in \Bbb C\setminus \{0\} (j=1,2,\dots ,n)$ are distinct complex constants, $p(z)$ is a polynomial, and ${\alpha }_{\lambda }(z) (\lambda \in I)$, ${a}_{i}(z) (i=0,1,\dots ,s)$, and ${b}_{j}(z) (j=0,1,\dots ,t)$ are small meromorphic functions relative to $f(z)$. We further investigate the above functional difference equation which has special type if its solution has Borel exceptional zero and pole.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 283895, 10 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412607223

Digital Object Identifier
doi:10.1155/2014/283895

Mathematical Reviews number (MathSciNet)
MR3200774

Zentralblatt MATH identifier
07022088

#### Citation

Huang, Zhi-Bo; Zhang, Ran-Ran. Some Properties on Complex Functional Difference Equations. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 283895, 10 pages. doi:10.1155/2014/283895. https://projecteuclid.org/euclid.aaa/1412607223