共查询到18条相似文献,搜索用时 93 毫秒
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本文研究亚纯系数的高阶线性微分方程,当方程系数满足一定条件时,得到方程的每一非零亚纯解具有无穷级且超级为n.此外,还研究了非齐次线性微分方程的亚纯解. 相似文献
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高凌云 《数学年刊A辑(中文版)》2014,35(2):193-202
研究了具有允许的亚纯解的复差分方程的形式以及系数的级与解的级两者的关系,得到了两个结果.将复微分方程中一些结果推广至复差分方程. 相似文献
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关于高阶线性微分方程亚纯解的增长率 总被引:32,自引:0,他引:32
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。 相似文献
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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. 相似文献
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This paper deals with the Briot-Bouquet differential equations with
degree three. The previous result shows that all the meromorphic
solutions belong to $W.$ Here, by applying the Kowalevski-Gambier
method, the authors give all the possible explicit meromorphic
solutions. The result is more applicable. Also, this method can be
used to deal with the more general Briot-Bouquet differential
equations. 相似文献
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本文讨论了两类具周期亚纯系数的微分方程(1.2),(1.3)亚纯解的表示,得到两个Malmqusit 型定理(定理1,定理3),即方程(1.2),(1.3)的亚纯解分别是其系数类的子类。 相似文献
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In this paper, by means of the normal family theory, we estimate the growth order of meromorphic solutions of some algebraic differential equations and improve the related result of Barsegian et al. [6]. We also give some examples to show that our results occur in some special cases. 相似文献
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Applying the Nevanlinna theory of meromorphic function,we investigate the non-admissible meromorphic solutions of nonlinear complex algebraic differential equation and gain a general result.Meanwhile,we prove that the meromorphic solutions of some types of the systems of nonlinear complex differential equations are non-admissible.Moreover,the form of the systems of equations with admissible solutions is discussed. 相似文献
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Zifeng Huang Liming Zhang Qiuhui Chen Wenjun Yuan 《Mathematical Methods in the Applied Sciences》2014,37(10):1553-1560
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. 相似文献
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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. 相似文献
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Cao Tingbin 《Annals of Differential Equations》2005,21(2):111-122
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. 相似文献