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- 저자 : BaoQin Chen (검색결과 2 건)
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MEROMORPHIC SOLUTIONS OF SOME q-DIFFERENCE EQUATIONS
Chen, Baoqin,Chen, Zongxuan Korean Mathematical Society 2011 대한수학회보 Vol.48 No.6
We consider meromorphic solutions of q-difference equations of the form $$\sum_{j=o}^{n}a_j(z)f(q^jz)=a_{n+1}(z),$$ where $a_0(z)$, ${\ldots}$, $a_{n+1}(z)$ are meromorphic functions, $a_0(z)a_n(z)$ ≢ 0 and $q{\in}\mathbb{C}$ such that 0 < |q| ${\leq}$ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0 < |q| < 1 and n = 2. Some growth estimates for meromorphic solutions are also given in the cases 0 < |q| < 1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q| = 1.
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Meromorphic solutions of some q-difference equations
BaoQin Chen,ZongXuan Chen 대한수학회 2011 대한수학회보 Vol.48 No.6
We consider meromorphic solutions of $q$-difference equations of the form [수식]=a_(n+1)(z), where a_0(z), ...,a_(n+1)(z) are meromorphic functions, a_0(z)a_n(z)[기호] 0 and q∈C such that 0<|q|≤ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0<|q|<1 and n=2. Some growth estimates for meromorphic solutions are also given in the cases 0<|q|<1 and |q|=1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q|=1.
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