arXiv subjects

Feng Lü

Publications and source records attributed to Feng Lü.

7 recordsLinked to original sources

arXiv2026

On entire solutions for a class of product-type nonlinear PDEs in $\mathbb{C}^n$

This paper is mainly devoted to describing the entire solutions of nonlinear partial differential equation $$ u_{z_1}u_{z_2}\cdots u_{z_n}=e^g, $$ with the eikonal equation as a prototype, where $g$ is a polynomial in $\mathbb{C}^n$. Through a novel method, we break through the restriction of finite order condition and present the explicit expressions for the entire solution of the above equation. As an application, we completely resolve two questions of Xu-Liu-Xuan in \cite{Xu}.

math.CV↗

arXiv2024

All meromorphic solutions of Fermat-type functional equations

In this paper, by making use of properties of elliptic functions, we describe meromorphic solutions of Fermat-type functional equations $f(z)^{n}+f(L(z))^{m}=1$ over the complex plane $\mathbb{C}$, where $L(z)$ is a nonconstant entire function, $m$ and $n$ are two positive integers. As applications, we also consider meromorphic solutions of Fermat-type difference and $q$-difference equations.

math.CV↗

arXiv2021

Meromorphic functions partially share three values with their difference operators

In this paper, we give a simple proof and strengthening of a uniqueness theorem of meromorphic functions which partially share 0, $\infty$ CM and 1 IM with their difference operators. Meanwhile, we partial solve a conjecture given by Chen-Yi in \cite{CY} and generalize some previous theorems in \cite{C, CX}.

math.CV↗

arXiv2020

The exact entire solutions of certain type of nonlinear difference equations

In this paper, we consider the entire solutions of nonlinear difference equation $$f^3+q(z)Δf=p_1 e^{α_1 z}+ p_2 e^{α_2 z} $$ where $q$ is a polynomial, and $p_1, p_2, α_1, α_2$ are nonzero constants with $α_1\neq α_2$. It is showed that if $f$ is a non-constant entire solution of $ρ_2(f)<1$ to the above equation, then $f(z)=e_1e^{\frac{α_1 z}{3}}+e_2e^{\frac{α_2 z}{3}}, $ where $e_1$ and $e_2$ are two constants. Meanwhile, we give an affirmative answer to the conjecture posed by Zhang et al in [18].

math.CV↗

arXiv2016

On the functional equation $f^n(z)+g^n(z)=e^{αz+β}$

We describe meromorphic solutions to the equations $f^n(z)+\left(f'\right)^n(z)=e^{αz+β}$ and $f^n(z)+f^n(z+c)=e^{αz+β}$ ($c\neq0$) over the complex plane $\mathbf{C}$ for integers $n\geq1$.

math.CV↗

arXiv2015

Meromorphic functions share three values with their difference operators

In the work, we focus on a conjecture due to Z.X. Chen and H.X. Yi[1] which is concerning the uniqueness problem of meromorphic functions share three distinct values with their difference operators. We prove that the conjecture is right for meromorphic function of finite order. Meanwhile, a result of J. Zhang and L.W. Liao[10] is generalized from entire functions to meromorphic functions.

math.CV↗

arXiv2014

A note on a famous theorem of Pang and Zalcman

In this paper, by studying the famous theorem of Pang and Zalcman, we find a normal family and obtain a result, which is an improvement of Pang and Zalcman's theorem in some sense. Meanwhile, several examples are provided to show that our result's conditions are necessary.

math.CV↗