Ahlfors' disc theorem for Riemann covering surfaces is extended to normally exhaustible Klein coverings.

A general example of an analytic function in the unit disc possessing an exceptional set in Nevanlinna’s second fundamental theorem is built. It is used to show that some conditions on the size of the exceptional set are sharp, extending analogous results for meromorphic functions in the plane.

This paper studies the uniqueness of meromorphic functions $$f^n\prod _{i=1}^k{\left(f^{\left(i\right)}\right)}^{n_i}\text{and}{g}^n\prod _{i=1}^k{\left(g^{\left(i\right)}\right)}^{n_i}$$ that share two values, where $n,n_k,k\in \mathbb{N}$, $n_i\in \mathbb{N}\cup \left\{0\right\}$, $i=1,2,...,k-1$. The results significantly rectify, improve and generalize the results due to Cao and Zhang (2012).

In the paper we consider the growth of entire solution of a nonlinear differential equation and improve some existing results.

In this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation $$\begin{array}{cc}& f^{\left(k\right)}+A_{k-1}{f}^{(k-1)}+\cdots +A_2{f}^{\text{'}\text{'}}+(D_1\left(z\right)+A_1\left(z\right){\mathrm{e}}^{az})f^{\text{'}}\hfill \\ & +(D_0\left(z\right)+A_0\left(z\right){\mathrm{e}}^{bz})f=F(k\ge 2),\hfill \end{array}$$ where $a$, $b$ are complex constants that satisfy $ab(a-b)\ne 0$ and $A_j\left(z\right)$$(j=0,1...$

We study the hyper-order of analytic solutions of linear differential equations with analytic coefficients having the same order near a finite singular point. We improve previous results given by S. Cherief and S. Hamouda (2021). We also consider the nonhomogeneous linear differential equations.

Let f(z), $z=r{e}^{i\theta }$, be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values $I_{\delta }\left(r\right)$ and the iterated mean values $N_{\delta ,k}\left(r\right)$ of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).

The main objective of this paper is to give the specific forms of the meromorphic solutions of the nonlinear difference-differential equation $$f^n\left(z\right)+P_d(z,f)=p_1\left(z\right){\mathrm{e}}^{{\alpha }_1\left(z\right)}+p_2\left(z\right){\mathrm{e}}^{{\alpha }_2\left(z\right)},$$ where $P_d(z,f)$ is a difference-differential polynomial in $f\left(z\right)$ of degree $d\le n-1$ with small functions of $f\left(z\right)$ as its coefficients, $p_1$, $p_2$ are nonzero rational functions and ${\alpha }_1$, ${\alpha }_2$ are non-constant polynomials. More precisely, we find out the conditions for ensuring the existence of meromorphic solutions of the above equation.