7 papers · 1 filter
On questions posed by Gundersen and Yang concerning a certain binomial differential equation
Xuxu Xiang, Jianren Long
Suppose \(a, b, c\) are polynomials with \(ab \neq 0\) and \(c\) nonconstant. We determine all entire solutions to the equation \begin{equation*} f'f'' - a(z)f^2 = b(z)e^{2c(z)}. \…
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…
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 f…
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 chara…
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…