Results 1 to 10 of about 577 (96)

A Simple Proof of the Chuang’s Inequality

Annals of the West University of Timisoara: Mathematics and Computer Science, 2017
The purpose of this paper is to present a short proof of the Chuang’s inequality.
Chakraborty Bikash
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Properties of meromorphic solutions of first-order differential-difference equations

Open Mathematics, 2023
For the first-order differential-difference equations of the form A(z)f(z+1)+B(z)f′(z)+C(z)f(z)=F(z),A\left(z)f\left(z+1)+B\left(z)f^{\prime} \left(z)+C\left(z)f\left(z)=F\left(z), where A(z),B(z),C(z)A\left(z),B\left(z),C\left(z), and F(z)F\left(z) are ...
Wu Lihao, Chen Baoqin, Li Sheng
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Uniqueness of exponential polynomials

Open Mathematics, 2023
In this article, we study the uniqueness of exponential polynomials and mainly prove: Let nn be a positive integer, let pi(z)(i=1,2,…,n){p}_{i}\left(z)\hspace{0.33em}\left(i=1,2,\ldots ,n) be nonzero polynomials, and let ci≠0(i=1,2,…,n){c}_{i}\ne 0 ...
Wang Ge, He Zhiying, Fang Mingliang
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Malmquist-type theorems on some complex differential-difference equations

Open Mathematics, 2022
This article is devoted to study the existence conditions of solutions to several complex differential-difference equations. We obtain some Malmquist theorems related to complex differential-difference equations with a more general form than the previous
Xu Hong Yan, Li Hong, Yu Meiying
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Meromorphic solutions of the (2 + 1)- and the (3 + 1)-dimensional BLMP equations and the (2 + 1)-dimensional KMN equation

Demonstratio Mathematica, 2021
The complex method is systematic and powerful to build various kinds of exact meromorphic solutions for nonlinear partial differential equations on the complex plane C{\mathbb{C}}.
Dang Guoqiang
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Unicity of meromorphic functions concerning differences and small functions

Open Mathematics, 2022
In this paper, we study the unicity of meromorphic functions concerning differences and small functions and mainly prove two results: 1. Let ff be a transcendental entire function of finite order with a Borel exceptional entire small function a(z)a\left ...
He Zhiying, Xiao Jianbin, Fang Mingliang
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Entire solutions for several complex partial differential-difference equations of Fermat type in ℂ2

Open Mathematics, 2021
By utilizing the Nevanlinna theory of meromorphic functions in several complex variables, we mainly investigate the existence and the forms of entire solutions for the partial differential-difference equation of Fermat type α∂f(z1,z2)∂z1+β∂f(z1,z2)∂z2m+f(
Gui Xian Min, Xu Hong Yan, Tang Wen Ju, Wang Hua   +3 more
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Uniqueness on entire functions and their nth order exact differences with two shared values

Open Mathematics, 2020
Let f(z) be an entire function of hyper order strictly less than 1. We prove that if f(z) and its nth exact difference Δcnf(z){\Delta }_{c}^{n}f(z) share 0 CM and 1 IM, then Δcnf(z)≡f(z){\Delta }_{c}^{n}f(z)\equiv f(z).
Chen Shengjiang, Xu Aizhu
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Meromorphic solutions of a third order nonlinear differential equation [PDF]

, 2010
We prove that all the meromorphic solutions of the nonlinear differential equation c0 u"' + 6 u^4 + c1 u" + c2 u u' + c3 u^3 + c4 u'+ c5 u^2 + c6 u +c7=0 are elliptic or degenerate elliptic, and we build them explicitly.Comment: 12 pages, to appear ...
Conte, Robert, Tuen-Wai, Ng
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Entire functions that share two pairs of small functions

Open Mathematics, 2021
In this paper, we study the unicity of entire functions and their derivatives and obtain the following result: let ff be a non-constant entire function, let a1{a}_{1}, a2{a}_{2}, b1{b}_{1}, and b2{b}_{2} be four small functions of ff such that a1≢b1{a}_ ...
Huang Xiaohuang, Deng Bingmao, Fang Mingliang   +2 more
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