대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제51권6호
  • /
  • Pages.1735-1748
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  • 2014
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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MEROMORPHIC SOLUTIONS OF A COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE

  • Zhang, Ran-Ran (Department of Mathematics Guangdong University of Education) ;
  • Huang, Zhi-Bo (School of Mathematical Sciences South China Normal University)
  • 투고 : 2013.11.12
  • 발행 : 2014.11.30
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초록

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).

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참고문헌

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