6 papers
A study on entire functions sharing one function with their difference operators and its application
Xuxu Xiang, Jianren Long
Let be a transcendental entire function with hyper-order strictly less than 1 and having a Borel exceptional small function. If and , or and , share a…
A problem of Heittokangas-Ishizaki-Tohge-Wen concerning a certain differential-difference equation
Xuxu Xiang, Jianren Long
All the finite order entire solutions of \begin{equation*} f^n(z)+q(z)e^{Q(z)}f^{(k)}(z+c)=P(z) \end{equation*} are given, where , are polynomials, and…
On Meromorphic Solutions to a Difference Equation of Tumura-Clunie Type
Jianren Long, Xuxu Xiang
The meromorphic solutions with of the non-linear difference equation \begin{align*} f^n(z)+P_d(z,f)=p_1e^{{λ_1}z}+p_2e^{{λ_2}z}+p_3e^{{λ_3}z}, \end{align*} are c…
Some new findings concerning value distribution of a pair of delay-differential polynomials
Jianren Long, Xuxu Xiang
The paired Hayman's conjecture of different types are considered. More accurately speaking, the zeros of a pair of and are characterized using…
On meromorphic solutions of Fermat type delay-differential equations with two exponential terms
Xuxu Xiang, Jianren Long, Mengting Xia +1
The existence of the meromorphic solutions to Fermat type delay-differential equation \begin{equation} f^n(z)+a(f^{(l)}(z+c))^m=p_1(z)e^{a_1z^k}+p_2(z)e^{a_2z^k}, \nonumber \end{eq…
On a question of Gundersen-Yang concerning entire solutions of binomial differential equations
Jianren Long, Mengting Xia, Xuxu Xiang
We study the question posed by G. Gundersen and C. C. Yang, in which the following two types of binomial differential equations are investigated, $$ a(z)f'f''-b(z)(f)^{2}=c(z)e^{2d…