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2014 Some Properties on Complex Functional Difference Equations
Zhi-Bo Huang, Ran-Ran Zhang
Abstr. Appl. Anal. 2014(SI14): 1-10 (2014). DOI: 10.1155/2014/283895

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.

Citation

Zhi-Bo Huang. Ran-Ran Zhang. "Some Properties on Complex Functional Difference Equations." Abstr. Appl. Anal. 2014 (SI14) 1 - 10, 2014. https://doi.org/10.1155/2014/283895

Information

Published: 2014
First available in Project Euclid: 6 October 2014

zbMATH: 07022088
MathSciNet: MR3200774
Digital Object Identifier: 10.1155/2014/283895