In this paper, we investigate the complex oscillation of differential polynomials generated by meromorphic solutions of differential equations

$$f^{(k)}+A(z)f=0,\quad k\geq 2,$$

where the coefficient 𝐴 is meromorphic in the unit disc $\mathbb{D}=\{z:|z| < 1\}$.

In this paper, we consider the zero distributions of 𝑞-shift difference polynomials of meromorphic functions with zero order, and obtain two theorems that extend the classical Hayman results on the zeros of differential polynomials to 𝑞-shift difference polynomials. We also investigate the uniqueness problem of 𝑞-shift difference polynomials that share a common value.

The purpose of this article is to investigate the uniqueness of meromorphic functions that share three or two finite sets on annuli.

In this paper, we investigate the value distribution of 𝑞-difference polynomials of meromorphic function of finite logarithmic order, and study the zero distribution of difference-differential polynomials $[f^{n}(z)f (qz + c)]^{(k)}$ and $[f^{n}(z)(f (qz + c) - f (z))]^{(k)}$, where $f(z)$ is a transcendental function of zero order. The uniqueness problem of difference-differential polynomials is also considered.