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THE EXACT MEROMORPHIC SOLUTIONS OF SOME NONLINEAR DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 2024年第1期44卷 103-114页

作者：刘慧芳毛志强 School of Mathematics and Statistics Jiangxi Normal UniversityNanchang330022China School of Mathematics and Computer Jiangxi Science and Technology Normal UniversityNanchang330038China

We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.

关键词： nevanlinna theory nonlinear differential equations meromorphic functions entire functions

QUASIPERIODICITY OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS

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Acta Mathematica Scientia 2024年第1期44卷 161-172页

作者：刘新玲刘凯 Risto KORHONEN Galina FILIPUK Department of Mathematics Nanchang UniversityNanchang330031China Department of Physics and Mathematics University of Eastern FinlandP.O.Box 11180101JoensuuFinland Institute of Mathematics Faculty of MathematicsInformatics and MechanicsUniversity of WarsawBanacha 202-097WarsawPoland

This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities... 详细信息

关键词： quasiperiodicity meromorphic functions complex delay-differential polynomials nevanlinna theory

Entire Solutions of Some Type of Nonlinear Delay-Differential Equations

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Journal of Mathematical Research with Applications 2024年第3期44卷 325-336页

作者： Qian YANG Huifang LIU School of Mathematics and Statistics Jiangxi Normal University

In this paper, the existence and growth of entire solutions of some type of nonlinear delay-differential equations are studied. Using Cartan's second main theorem and nevanlinna theory of meromorphic functions, we obt... 详细信息

关键词： nevanlinna theory differential equation delay-differential equation entire solution

Holomorphic Curves into Projective Varieties Intersecting Closed Subschemes in Subgeneral Position

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Chinese Annals of Mathematics,Series B 2022年第6期43卷 1023-1032页

作者： Qingchun JI Jun YAO Guangsheng YU School of Mathematical Sciences and Shanghai Center for Mathematical Sciences Fudan UniversityShanghai 200433China School of Mathematical Sciences Fudan UniversityShanghai 200433China School of Mathematics and Statistics Ningbo UniversityNingbo 315211China

In this paper,the authors introduce the index of subgeneral position for closed subschemes and obtain a second main theorems based on this *** also give the corresponding Schmidt’s subspace type theorem via the analo... 详细信息

关键词： nevanlinna theory Second main theorem Holomorphic curve Subgeneral position Closed subschemes Schmidt’s subspace theorem

RESULTS ON A QUESTION OF ZHANG AND YANG

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Acta Mathematica Scientia 2012年第2期32卷 717-723页

作者：李升高宗升 LMIB&School of Mathematics and Systems Science Beihang University College of Science Guangdong Ocean University

For a meromorphic function f, let N（l＋1（r, 3） denote the counting function of zeros of f of order 1 at least. Let f be a nonconstant meromorphic function, such that N（r,f） =S（r,f）. Denote F = fn. Suppose that F andF＇ share 1 CM. If（l） n 〉 3, or （2） n = 2 and N（r, 3） = O（N（3（r, 1/f））, then, F = F＇, and f assumes the form l（z） = ce 1/nz where c is a nonzero constant. This main result of this article gives a positive answer to a question raised by Zhang and Yang [1] for the meromorphic functions case in some sense. And a relative result is proved.

关键词： nevanlinna theory shared value derivative

An improvement of Chen-Ru-Yan's degenerated second main theorem

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Science China Mathematics 2015年第12期58卷 2517-2530页

作者： SHI Lei RU Min Department of Mathematics East China Normal University Department of Mathematics University of Houston

We give an improvement for the second main theorem of algebraically non-degenerate holomorphic curves into a complex projective variety V intersecting hypersurfaces in subgeneral position, obtained by Chen et al.(2012... 详细信息

关键词： nevanlinna theory holomorphic curve second main theorem truncation level

Radically distributed value and normal families of meromorphic functions

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Frontiers of Mathematics in China 2014年第2期9卷 355-376页

作者： Jianming QI Guowei ZHANG Weniun YUAN Department of Mathematics and Physics Shanghai Dianji University Shanghai 200240 China School of Mathematics and Information Sciences Guangzhou UniversityGuangzhou 510006 China Department of Mathematics Anyang Normal University Anyang 455000 China Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes Guangzhou University Guangzhou 510006 China

We establish several upper-bound estimates for the growth of meromorphic functions with radially distributed value. We also obtain a normality criterion for a class of meromorphic functions, where any two of whose dif... 详细信息

关键词： Meromorphic function nevanlinna theory normal family angular characteristic function radially distributed value

Weak Cartan-type Second Main Theorem for Holomorphic Curves

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Acta Mathematica Sinica,English Series 2008年第3期24卷 455-462页

作者： Qi Ming YAN Zhi Hua CHEN Department of Mathematics Tongji University Shanghai 200092 P. R. China

In this paper, a weak Cartan-type second theorem for holomorphic curve f ： C→P^n（C） intersecting hypersurfaces Dj, 1≤j≤q, in P^n（C） in general position with degree dj is given as follows： For every ε〉0, there exists a positive integer M such that ｜｜（q - （n ＋ 1） ε）Tf（r）≤∑j^q=1 1/dj Nf^M（r,Dj）＋o（Tf（r））, where ＂｜｜＂ means the estimate holds for all large r outside a set of finite Lebesgue measure.

关键词： holomorphic curve nevanlinna theory second main theorem hypersurface

Cartan's Second Main Theorem and Mason's Theorem for Jackson Difference Operator

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Chinese Annals of Mathematics,Series B 2022年第3期43卷 383-400页

作者： Huixin DAI Tingbin CAO Yezhou LI School of Science Beijing University of Posts and TelecommunicationsBeijing 100876China Department of Mathematics Nanchang UniversityNanchangJiangxi 330031China

Let f:C→P^(n)be a holomorphic curve of order *** authors establish a Jackson difference analogue of Cartan’s second main theorem for the Jackson q-Casorati determinant and introduce a truncated second main theorem of Jackson difference operator for holomorphic *** addition,a Jackson difference Mason’s theorem is proved by using a Jackson difference radical of a ***,they extend the Mason’s theorem for m+1 *** examples are constructed to show that their results are accurate.

关键词： Jackson difference operator nevanlinna theory Holomorphic curve Cartan’s second main theorem Mason’s theorem Polynomial