Results 1 to 10 of about 115 (110)
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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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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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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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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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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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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Uniqueness of meromorphic functions sharing two finite sets
Open Mathematics, 2017 We prove uniqueness theorems of meromorphic functions, which show how two meromorphic functions are uniquely determined by their two finite shared sets. This answers a question posed by Gross.
Chen Jun-Fan
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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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