Complex Difference Equations of Malmquist Type
Complex Difference Equations of Malmquist Type
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DOI：
10.1007/bf03320974
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发表时间：
2001-09
影响因子：
2.1
通讯作者：
J. Heittokangas;R. Korhonen;I. Laine;J. Rieppo;K. Tohge
中科院分区：
文献类型：
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作者：
J. Heittokangas;R. Korhonen;I. Laine;J. Rieppo;K. Tohge
在最近的一篇论文[1]中，Ablowitz，Halburd和Herbst应用Nevanlinna理论证明了复差分方程的一些结果，这使人想起复微分方程中的经典Malmquist定理。他们的结果的一个典型例子告诉我们，如果复差分方程y（z+ 1）+y（z− 1）=R（z，y）且R（z，y）在两个自变量中都有理，则degyR（z，y）≤ 2。本文改进和推广了这些结果。除了阶的考虑，一个结果（见定理13）被证明表明，具有Borel例外的零和极点的解决方案似乎只出现在特殊情况下。
In a recent paper [1], Ablowitz, Halburd and Herbst applied Nevanlinna theory to prove some results on complex difference equations reminiscent of the classical Malmquist theorem in complex differential equations. A typical example of their results tells us that if a complex difference equationy(z+ 1) +y(z− 1) =R(z, y) withR(z, y) rational in both arguments admits a transcendental meromorphic solution of finite order, then degyR(z, y) ≤ 2. Improvements and extensions of such results are presented in this paper. In addition to order considerations, a result (see Theorem 13) is proved to indicate that solutions having Borel exceptional zeros and poles seem to appear in special situations only.