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MEROMORPHIC SOLUTIONS OF A COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE

  • Zhang, Ran-Ran ;
  • Huang, Zhi-Bo
  • Received : 2013.11.12
  • Published : 2014.11.30

Abstract

In this paper, we investigate the finite order transcendental meromorphic solutions of complex difference equation of Malmquist type $$\prod_{i=1}^{n}f(z+c_i)=R(z,f)$$, where $c_1,{\ldots},c_n{\in}\mathbb{C}{\backslash}\{0\}$, and R(z, f) is an irreducible rational function in f(z) with meromorphic coefficients. We obtain some results on deficiencies of the solutions. Using these results, we prove that the growth order of the finite order solution f(z) is 1, if f(z) has Borel exceptional values $a({\in}\mathbb{C})$ and ${\infty}$. Moreover, we give the forms of f(z).

Keywords

difference equation;meromorphic function;deficiency

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Acknowledgement

Supported by : National Natural Science Foundation of China, Natural Science Foundation of Guangdong Province in China