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Exact forms of entire solutions for Fermat type partial differential equations in C^2 [PDF]

Electronic Journal of Differential Equations, 2021
This article studies the existence and the exact form of entire solutions of several Fermat type partial differential equations in \(\mathbb{C}^2\), by utilizing the Nevanlinna theory of meromorphic functions in several complex  variables.
Yu Xian Chen, Hong Yan Xu
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Characterizations of entire solutions for the system of Fermat-type binomial and trinomial shift equations in ℂn#

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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Entire Solutions of the Second-Order Fermat-Type Differential-Difference Equation

Journal of Mathematics, 2020
In this paper, the entire solutions of finite order of the Fermat-type differential-difference equation f″z2+△ckfz2=1 and the system of equations f1″z2+△ckf2z2=1 and f2″z2+△ckf1z2=1 have been studied.
Guoqiang Dang, Jinhua Cai
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Results on Solutions for Several Systems of Partial Differential-Difference Equations with Two Complex Variables

Journal of Mathematics, 2023
This article is to describe the entire solutions of some partial differential-difference equations and systems. Some theorems about the forms of transcendental entire solutions with finite order for several high-order partial differential-difference ...
Yuxian Chen, Libing Xie, Hongyan Xu
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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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Solutions of complex nonlinear functional equations including second order partial differential and difference in C^2

Electronic Journal of Differential Equations, 2023
This article is devoted to exploring the existence and the form of finite order transcendental entire solutions of Fermat-type second order partial differential-difference equations $$ \Big(\frac{\partial^2 f}{\partial z_1^2}+\delta\frac{\partial^2 f ...
Hong Yan Xu, Goutam Haldar
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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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The study of solutions for several systems of PDDEs with two complex variables

Demonstratio Mathematica, 2023
The purpose of this article is to describe the properties of the pair of solutions of several systems of Fermat-type partial differential difference equations.
Xu Yi Hui, Liu Xiao Lan, Xu Hong Yan
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Entire solutions for several second-order partial differential-difference equations of Fermat type with two complex variables

Advances in Difference Equations, 2021
This paper is concerned with description of the existence and the forms of entire solutions of several second-order partial differential-difference equations with more general forms of Fermat type.
Hong Yan Xu, Da Wei Meng, Sanyang Liu, Hua Wang   +3 more
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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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