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Subnormal solutions of differential equations with periodic coefficients
Zongxuan, C.,Kwangho, S. Science Press 2010 Acta mathematica scientia Vol.30 No.1
In this article, we apply the concept of hyper-order to higher order linear differential equations with periodic coefficients, investigate the existence and the form of its subnormal solution, and estimate the growth of all other solutions, and answer the question raised by Gundersen and Steinbart for more general periodic differential equations.
Estimates for the zeros of differences of meromorphic functions
Chen, ZongXuan,Shon, Kwang Ho Springer-Verlag 2009 Science in China. Series A, Mathematics Vol.52 No.11
<P>Let f be a transcendental meromorphic function and g(z) = f (z + c(1)) + f(z + c(2)) - 2f(z) and g(2) (z) = f (z + c(1)) . f (z + c(2)) - f(2)(z). The exponents of convergence of zeros of differences g(z), g(2)(z), g(z)/f(z), and g(2)(z)/f(2)(z) are estimated accurately.</P>
THE ZEROS DISTRIBUTION OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS IN AN ANGULAR DOMAIN
Zhibo Huang,Zongxuan Chen 대한수학회 2010 대한수학회보 Vol.47 No.3
In this paper, we investigate the zeros distribution and Borel direction for the solutions of linear homogeneous differential equation f(n) + An−2(z)f(n−2) + · · · + A1(z)f' + A0(z)f = 0 (n ≥ 2)in an angular domain. Especially, we establish a relation between a cluster ray of zeros and Borel direction.
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.
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.
THE ZEROS DISTRIBUTION OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS IN AN ANGULAR DOMAIN
Huang, Zhibo,Chen, Zongxuan Korean Mathematical Society 2010 대한수학회보 Vol.47 No.3
In this paper, we investigate the zeros distribution and Borel direction for the solutions of linear homogeneous differential equation $f^{(n)}+A_{n-2}(z)f^{(n-2)}+{\cdots}+A_1(z)f'+A_0(z)f=0(n{\geq}2)$ in an angular domain. Especially, we establish a relation between a cluster ray of zeros and Borel direction.