共查询到19条相似文献,搜索用时 81 毫秒
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运用Nevanlinna理论研究亚纯函数差分多项式的值分布和唯一性,改进了先前已知的一些结果. 相似文献
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主要运用Nevanlinna值分布理论,研究了一类关于超越亚纯函数的复差分-微分多项式的零点问题,推广了差分-微分多项式的一些结果.利用分析函数的零点与极点的方法,证明了n取一定值时,复差分-微分多项式取零点无穷多次,结果可被看作Hayman猜想的微分-差分形式. 相似文献
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Halburd和Korhonen指出研究复域差分的值分布问题对进一步研究复域差分与差分方程具有十分重要的意义.本文得到了关于有限级亚纯函数的差分多项式的亏量为一些结果,其中部分结果可视为微分多项式相应结果的差分模拟.同时,我们在一定条件下给出了经典的Valiron-Mohon'ko定理的一个差分模拟结果,并且作为本文中的一个重要工具出现.这些结果推广了前人已有结果. 相似文献
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本文利用亚纯函数的Nevanlinna值分布理论,研究亚纯函数差分的值分布问题,得到亚纯函数差分的值分布问题,推广和改进一些文献中的结论,得到三个结果. 相似文献
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假设函数f(z)是亚纯函数,H(z,f)是关于f(z)的差分多项式,s(z)是关于f(z)的小函数,考察了差分多项式f(z)~nH(z,f)-s(z)的零点分布问题.首先得到了差分多项式f(z)~nH(z,f)-s(z)的零点计数函数和函数f(z)的特征函数以及极点计数函数之间的一些不等式估计,再根据这些不等式,建立了Hayman关于亚纯函数的一个经典结果的差分模拟. 相似文献
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文中利用亚纯函数Nevanlina理论和复差分理论,研究一类复差分方程组有限级非亚纯允许解的存在性问题.同时,讨论了这类复差分方程组存在有限级亚纯允许解时方程组的形式. 相似文献
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In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible. 相似文献
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In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible. 相似文献
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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 amongδ(∞,f),δ(∞,f′),δ(∞,f(z)nf(qz+c)mf′(z)),δ(∞,f(qz+c);f′(z))andδ(∞,f(z)nf(qz+c)m). 相似文献
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Nan Li 《Journal of Difference Equations and Applications》2013,19(2):237-250
In this paper, we investigate the complex oscillation problems of meromorphic solutions to some linear difference equations with meromorphic coefficients, and obtain some results about the relationships between the exponent of convergence of zeros, poles and the order of growth of meromorphic solutions to complex linear difference equations. We also study the existence of solution of certain types of nonlinear differential-difference equations, and partially answer a conjecture concerning the above problem posed by Yang and Laine (C.C. Yang and I. Laine, On analogies between nonlinear difference and differential equations, Proc. Japan Acad. Ser. A Math. Sci. 86(1) (2010), pp. 10–14). 相似文献
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Kai Liu 《Results in Mathematics》2010,57(3-4):365-376
This research is a continuation of a recent paper, due to Liu and Laine, dealing with difference polynomials of entire function. In this paper, we investigate the value distribution of difference polynomials of meromorphic functions and prove some difference analogues to some classical results for differential polynomials. 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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In this paper, we consider the zero distributions of q-shift difference polynomials of meromorphic functions with zero order, and obtain two theorems that extend the classical
Hayman results on the zeros of differential polynomials to q-shift difference polynomials. We also investigate the uniqueness problem of q-shift difference polynomials that share a common value. 相似文献
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Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations 总被引:1,自引:0,他引:1
R.G. Halburd 《Journal of Mathematical Analysis and Applications》2006,314(2):477-487
The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is presented and then applied to prove a number of results on meromorphic solutions of complex difference equations. These results include a difference analogue of the Clunie lemma, as well as other results on the value distribution of solutions. 相似文献
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We study the value distribution of difference polynomials of meromorphic functions, and extend classical theorems of Tumura-Clunie type to difference polynomials. We also consider the value distribution of f (z)f (z + c). 相似文献