Results 1 to 10 of about 929 (107)
A Simple Proof of the Chuang’s Inequality [PDF]
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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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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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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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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On the equation fn + (f″)m ≡ 1
Demonstratio Mathematica, 2023 Let nn and mm be two positive integers, and the second-order Fermat-type functional equation fn+(f″)m≡1{f}^{n}+{({f}^{^{\prime\prime} })}^{m}\equiv 1 does not have a nonconstant meromorphic solution in the complex plane, except (n,m)∈{(1,1),(1,2),(1,3 ...
Dang Guoqiang
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Open Mathematics, 2023 Our purpose in this article is to describe the solutions of several product-type nonlinear partial differential equations (PDEs) (a1u+b1uz1+c1uz2)(a2u+b2uz1+c2uz2)=1,\left({a}_{1}u+{b}_{1}{u}_{{z}_{1}}+{c}_{1}{u}_{{z}_{2}})\left({a}_{2}u+{b}_{2}{u}_{{z}_{
Xu Yi Hui +3 more
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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 solutions of two certain Fermat-type ordinary differential equations
Open Mathematics, 2023 In this article, we investigate the precise expression forms of entire solutions for two certain Fermat-type ordinary differential equations: (a0f+a1f′)2+(a0f+a2f′)2=p{\left({a}_{0}f+{a}_{1}{f}^{^{\prime} })}^{2}+{\left({a}_{0}f+{a}_{2}{f}^{^{\prime} })}^
Hu Binbin, Yang Liu
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Demonstratio Mathematica, 2023 In this article, we investigate the existence and the precise form of finite-order transcendental entire solutions of some system of Fermat-type quadratic binomial and trinomial shift equations in Cn{{\mathbb{C}}}^{n}. Our results are the generalizations
Haldar Goutam, Banerjee Abhijit
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