几类高阶线性微分方程亚纯解的增长性

本文研究了几类亚纯函数系数的高阶线性微分方程解的增长性问题,得到了齐次和非齐次线性微分方程亚纯解增长性的精确估计.     

一类高阶微分方程亚纯解的增长性

研究了几种类型的高阶线性亚纯系数微分方程的亚纯解的增长性,对方程的亚纯解的增长率得到了精确估计.     

关于高阶线性微分方程亚纯解的增长率

本文研究了二种类型的高阶线性齐次亚纯函数系数微分方程的亚纯解的增长性,当存在某个系数对方程的解的性质起主要支配作用时,我们对方程的亚纯解的增长率得到了精确的估计。     

一类高阶微分方程亚纯解的下级、超级、二级不同零点收敛指数

本文研究了一类高阶亚纯系数非齐次及齐次线性微分方程的复振荡.在亚纯解的极点重数无限制的前提下,得到了方程亚纯解的下级、超级、二级不同零点收敛指数等的精确估计.改进了陈宗煊、Ki-HoKwon等的结果.     

关于某类Briot-Bouquet微分方程若干结果的推广

本文研究了某类形式的Briot-Bouquet微分方程的亚纯解结构问题.利用Nevanlinna值分布理论的有关知识,获得了该类微分方程的所有可能形式,以及当方程的阶为偶数时,给出了每一个形式的方程的亚纯解结构,推广了某些特定的Briot-Bouquet微分方程亚纯解结构的一些结果.     

某类线性微分方程亚纯解的增长性

研究了一类亚纯函数系数的线性微分方程的解的增长性问题,得到了齐次和非齐线性微分方程亚纯解的增长级、超级、二级不同零点收敛指数的精确估计．     

复高阶微分方程的解

利用亚纯函数的Nevanlinna值分布理论以及最大模原理,讨论了一类复高阶微分方程的代数体解以及一类复高阶微分方程组的超越亚纯解的存在性问题,得到了两个结论.还推广了一些文献的结论,例子表明该文的结论是精确的.     

两类破碎群体平衡方程接受的李群及群不变解

针对难找到破碎群体平衡方程的精确解和解析方法缺乏的问题,研究两类积分-偏微分方程(破碎群体平衡方程)接受的李群、群不变解、约化积分-常微分方程及精确解.首先采用伸缩变换李群分析方法探寻积分-偏微分方程接受的李群.其次将积分-偏微分方程转化为纯偏微分方程,运用经典李群分析方法计算纯偏微分方程接受的李群.然后利用改进了的李群分析方法结合伸缩变换群和经典李群分析方法获得的结果确定积分-偏微分方程接受的李群.最后找到了积分-偏微分方程接受的李群,给出了积分-偏微分方程的约化积分-常微分方程、群不变解及显式精确解,分析了部分解的动力学行为性质及特征.     

某类差分方程亚纯解的增长性

本文研究了某类差分方程的亚纯解的增长性问题及不存在可允许超越亚纯解的条件.运用Nevanlinna理论的基本方法,得到了当p(z)为多项式时此类差分方程亚纯解的级与下级的估计,并给出了一些例子说明这些结果是精确的.     

高阶代数微分方程解的增长级(英文)

本文研究了高阶代数微分方程解的增长级的问题.利用亚纯函数的Nevanlinna值分布理论和微分方程的一些技巧,得到了一个更精确和更一般的结论,推广了何育赞和Laine的一些理论.     

The representation of meromorphic solutions for a class of odd order algebraic differential equations and its applications

In this paper, we employ the Nevanlinna's value distribution theory to investigate the existence of meromorphic solutions of algebraic differential equations. We obtain the representations of all meromorphic solutions for a class of odd order algebraic differential equations with the weak ?p,q?and dominant conditions. Moreover, we give the complex method to find all traveling wave exact solutions of corresponding partial differential equations. As an example, we obtain all meromorphic solutions of the Kuramoto–Sivashinsky equation by using our complex method. Our results show that the complex method provides a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics. Copyright © 2014 John Wiley & Sons, Ltd.     

All meromorphic solutions of an ordinary differential equation and its applications

Dedicated to Professor Yuzan He on the Occasion of his 80th Birthday In this paper, we employ the complex method to obtain all meromorphic solutions of an auxiliary ordinary differential equation at first and then find out all meromorphic exact solutions of the combined KdV–mKdV equation and variant Boussinesq equations. Our result shows that all rational and simply periodic exact solutions of the combined KdV–mKdV equation and variant Boussinesq equations are solitary wave solutions, the method is more simple than other methods, and there exist some rational solutions w_r,2(z) and simply periodic solutions w_s,2(z) that are not only new but also not degenerated successively by the elliptic function solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

Meromorphic solutions of an auxiliary ordinary differential equation using complex method

In this paper, we employ the complex method to obtain first all meromorphic solutions of an auxiliary ordinary differential equation and then find all meromorphic exact solutions of the classical Korteweg–de Vries equation, Boussinesq equation, ( 3 + 1)‐dimensional Jimbo–Miwa equation, and Benjamin–Bona–Mahony equation. Our results show that the method is more simple than other methods. Copyright © 2013 John Wiley & Sons, Ltd.     

All Meromorphic Solutions of Some Algebraic Differential Equations

In this article, we introduce some results with respect to the integrality and exact solutions of some 2nd order algebraic DEs. We obtain the sufficient and necessary conditions of integrable and the general meromorphic solutions of these equations by the complex method, which improves the corresponding results obtained by many authors. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics.     

Meromorphic solutions of some algebraic differential equations related Painlevé equation IV and its applications

In this paper, the complex method is used to derive meromorphic solutions to some algebraic differential equations related Painlevé equation IV, and then we illustrate our main result by some computer simulations. By the application of our result, we obtain meromorphic solutions of a nonlinear evolution equation. We can apply the idea of this study for other nonlinear evolution equations in mathematical physics.     

Meromorphic exact solutions of the generalized (3+1)-dimensional Kadomtsev-Petviashvili equations

In this work, the generalized (3+1)-dimensional Kadomtsev-Petviashvili equation and its new form have been systematically investigated by using the complex method. The method is based on complex analysis and complex differential equations. And we get plentiful meromorphic exact solutions of these equations, which include rational solutions, exponential function solutions, and elliptic function solutions. The dynamic behaviors of these solutions are also shown by some graphs.     

复微分方程组亚纯解的分量的Nevanlinna特征估计

本文讨论了一类复微分方程组的亚纯解的分量的Nevanlinna特征估计,利用亚纯函数Nevanlinna值分布理论,得到了一个有关方程组亚纯解的分量的Nevanlinna特征估计定理.该结果推广了高凌云等人的一些结果.     

ON THE ITERATED ORDER OF MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.     

一类亚纯系数微分方程解的增长性

研究了一类亚纯系数微分方程的复振荡问题.通过应用亚纯函数的分解和模的增长估计,得到了该类方程解的级及其超级的精确估计.     

Unicity of meromorphic solutions of partial differential equations

In this survey, results on the existence, growth, uniqueness, and value distribution of meromorphic (or entire) solutions of linear partial differential equations of the second order with polynomial coefficients that are similar or different from that of meromorphic solutions of linear ordinary differential equations have been obtained. We have characterized those entire solutions of a special partial differential equation that relate to Jacobian polynomials. We prove a uniqueness theorem of meromorphic functions of several complex variables sharing three values taking into account multiplicity such that one of the meromorphic functions satisfies a nonlinear partial differential equations of the first order with meromorphic coefficients, which extends the Brosch??s uniqueness theorem related to meromorphic solutions of nonlinear ordinary differential equations of the first order.