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Journal of Mathematical Research with Applications 2020年第5期40卷 507-518页

作者： Hongyan XU xiumin zheng School of Mathematics and Computer Science Shangrao Normal University Department of Mathematics Jiangxi Normal University

In this paper, we mainly investigate some properties of meromorphic solutions for several q-difference equations, which can be seen as the q-difference analogues of Painlevé equations. Some results about the existence and the estimates of growth of meromorphic solution f for q-difference equations are obtained, especially for some estimates for the exponent of convergence of poles of ?qf(z) := f(qz)-f(z), which extends some previous results by Qi and Yang.

关键词： meromorphic function $q$-difference equation zero order

The Zeros and Nevanlinna Deficiencies for Some q-Shift Difference Differential Polynomials of Meromorphic Functions

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Journal of Mathematical Research with Applications 2022年第1期42卷 31-40页

作者： xiumin zheng Hongyan XU School of Mathematics and Statistics Jiangxi Normal University School of Mathematics and Computer Science Shangrao Normal University

The first purpose of this paper is to study the properties on some q-shift difference differential polynomials of meromorphic functions, some theorems about the zeros of some q-shift difference-differential polynomials with more general forms are obtained. The second purpose of this paper is to investigate the properties on the Nevanlinna deficiencies for q-shift difference differential monomials of meromorphic functions, we obtain some relations among δ(∞, f),δ(∞, f′), δ(∞, f(z)nf(qz + c)~mf′(z)), δ(∞, f(qz + c)~mf′(z)) and δ(∞, f(z)~nf(qz + c)~m).

关键词： Nevanlinna theory $q$-shift difference differential zero order

Growth of Meromorphic Solutions of Complex Linear Differential-Difference Equations with Coefficients Having the Same Order

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Journal of Mathematical Research with Applications 2014年第6期34卷 683-695页

作者： Shunzhou WU xiumin zheng Institute of Mathematics and Information Science Jiangxi Normal University

The main purpose of this paper is to study the growth of meromorphic solutions of complex linear differential-difference equations L(z, f) =n∑i=0m∑j=0Aij(z)f(j)(z + ci) = 0 or F(z)with entire or meromorphic coeffici... 详细信息

关键词： linear differential-difference equation meromorphic solution order lower order

HYPER ORDER OF SOLUTIONS TO SOME LINEAR DIFFERENTIAL EQUATIONS IN THE UNIT DISC

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Annals of Differential Equations 2013年第4期29卷 406-414页

作者： Jing He xiumin zheng Institute of Math. and Information Science Jiangxi Normal University

In this paper, we investigate the growth of solutions to some linear diferential equations with analytic coefcients in the unit disc. When the coefcients of these equations have some special properties near a point on the boundary of the unit disc, the order and the hyper order of the solutions to these equations are estimated accurately. Especially, our conditions on the coefcients are more general and the results on the hyper order of the solutions are new to some extent.

关键词： analytic function unit disc order hyper order

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SOLUTIONS TO LINEAR DIFFERENTIAL EQUATIONS WITH SOME COEFFICIENT BEING LACUNARY SERIES OF [p, q]-ORDER IN THE COMPLEX PLANE

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Annals of Differential Equations 2014年第3期30卷 364-372页

作者： Meilong Zhan xiumin zheng Institute of Math. and Information Science Jiangxi Normal University

In this paper, we investigate the growth and value distribution of meromorphic solutions to higher order linear differential equations with some dominating coefficient being Lacunary series and the results of this pap... 详细信息

关键词： linear differential equation meromorphic solution Lacunary series

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Hyper Order of Solutions of Higher Order L. D. E. with Coefficients Being Lacunary Series

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Journal of Mathematical Research with Applications 2012年第6期32卷 687-693页

作者： Jin TU , Jie JIANG, xiumin zheng School of Mathematics and Information Science, Jiangxi Normal University,Jiangxi 330022, P. R. China School of Mathematics and Information Science Jiangxi Normal University Jiangxi 330022

In this paper, we investigate the hyper order of the solutions of high order linear differential equations with some dominated coefficient being lacunary series, and obtain some results which improve and extend previo... 详细信息

关键词： linear differential equations hyper order lacunary series.