Results 41 to 50 of about 115 (110)

Results on the deficiencies of some differential-difference polynomials of meromorphic functions

Open Mathematics, 2016
In this paper, we study the relation between the deficiencies concerning a meromorphic function f(z), its derivative f′(z) and differential-difference monomials f(z)mf(z+c)f′(z), f(z+c)nf′(z), f(z)mf(z+c).
Zheng Xiu-Min, Xu Hong-Yan
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On meromorphic functions for sharing two sets and three sets in m-punctured complex plane

Open Mathematics, 2016
In this article, we study the uniqueness problem of meromorphic functions in m-punctured complex plane Ω and obtain that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 9, such that any two admissible meromorphic functions f and g in Ω must be ...
Xu Hong-Yan, Zheng Xiu-Min, Wang Hua
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On a question of Gundersen-Yang concerning entire solutions of binomial differential equations

Demonstratio Mathematica
The explicit forms of entire solutions of the binomial differential equationsa(z)f′f″−b(z)(f)2=c(z)e2d(z),a(z)ff′−b(z)(f″)2=c(z)e2d(z), $$a\left(z\right){f}^{\prime }{f}^{{\prime\prime}}-b\left(z\right){\left(f\right)}^{2}=c\left(z\right){e}^{2d\left(z ...
Long Jianren, Xia Mengting, Xiang Xuxu
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The existence of solutions to certain type of nonlinear difference-differential equations

Open Mathematics, 2018
In this paper we study the entire solutions to a certain type of difference-differential equations. We also give an affirmative answer to the conjecture of Zhang et al.
Lü Weiran, Wu Linlin, Wang Dandan, Yang Chungchun   +3 more
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Some results on the value distribution of differential polynomials

Open Mathematics, 2023
In this article, we study some results on the value distribution of differential polynomials and mainly prove the following theorem: suppose that PP is a polynomial with degP≥3{\rm{\deg }}\hspace{0.33em}P\ge 3 and ff is a transcendental meromorphic ...
Fan Jinyu, Xiao Jianbin, Fang Mingliang
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On Transcendental Entire Solution of Fermat-Type Trinomial and Binomial Equations Under Restricted Hyper-Order

Annales Mathematicae Silesianae
In this paper we are focusing on finding the transcendental entire solution of Fermat-type trinomial and binomial equations, by restricting the hyper-order to be less than one.
Banerjee Abhijit, Sarkar Jhuma
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Meromorphic exact solutions of the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

Open Mathematics, 2020
In this article, meromorphic exact solutions for the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff (gCBS) equation are obtained by using the complex method.
Aminakbari Najva, Gu Yongyi, Yuan Wenjun
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Uniqueness of meromorphic functions concerning small functions and derivatives-differences

Demonstratio Mathematica
In this article, we study the unicity of meromorphic functions concerning small functions and derivatives-differences. The results obtained in this article extend and improve some results of Chen et al.
He Zhiying, Fang Mingliang, Xiao Jianbin
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Results on solutions of several systems of the product type complex partial differential difference equations

Demonstratio Mathematica
This article is devoted to exploring the solutions of several systems of the first-order partial differential difference equations (PDDEs) with product type u(z+c)[α1u(z)+β1uz1+γ1uz2+α2v(z)+β2vz1+γ2vz2]=1,v(z+c)[α1v(z)+β1vz1+γ1vz2+α2u(z)+β2uz1+γ2uz2]=1 ...
Liu Xiao Lan, Xu Hong Yan, Xu Yi Hui, Li Nan   +3 more
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Solutions of several general quadratic partial differential-difference equations in ℂ2

Demonstratio Mathematica
In this article, we have introduced general transformation to solving the general quadratic equations. It is of interest to know about the existence and form of the solutions of general quadratic functional equations.
Ahamed Molla Basir, Mandal Sanju
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