相关论文: Zero order meromorphic solutions of $q$-difference…

It is shown that if It is shown that if \begin{equation}\label{abstract_eq} f(z+1)^n=R(z,f),\tag{\dag} \end{equation} where $R(z,f)$ is rational in $f$ with meromorphic coefficients and $\deg_f(R(z,f))=n$, has an admissible meromorphic…

Recently, the present authors used Nevanlinna theory to provide a classification for the Malmquist type difference equations of the form $f(z+1)^n=R(z,f)$ $(\dag)$ that have transcendental meromorphic solutions, where $R(z,f)$ is rational…

It is shown that if the equation \begin{equation*} f(z+1)^n=R(z,f), \end{equation*} where $R(z,f)$ is rational in both arguments and $\deg_f(R(z,f))\not=n$, has a transcendental meromorphic solution, then the equation above reduces into one…

In this paper, we use the Banach fixed point theorem to examine the existence of meromorphic solutions to the following first-order $q$-difference equation \begin{align}\tag{{\dag}}\label{dagger}…

In this paper, we study the following complex Schr\"{o}dinger equation with a $q$-difference term: \begin{align}\tag{{\dag}}\label{dagger} f'(z) = a(z)f(qz) + R(z, f(z)), \quad R(z, f(z)) = \frac{P(z, f(z))}{Q(z, f(z))}, \end{align} where…

Let w(z) be a finite-order meromorphic solution of the second-order difference equation w(z+1)+w(z-1) = R(z,w(z)) (eqn 1) where R(z,w(z)) is rational in w(z) and meromorphic in z. Then either w(z) satisfies a difference linear or Riccati…

In this article, we construct explicit meromorphic solutions of first order linear $q$-difference equations in the complex domain and we describe the location of all their zeros and poles. The homogeneous case leans on the study of four…

In this paper, we study a Malmquist-Yosida type theorem for Schwarzian differential equations \begin{equation}\label{1} S(f,z)^{m} = R(z,f) = \frac{P(z,f)}{Q(z,f)},\tag{+} \end{equation} where $m \in \mathbb{N}^{+}$, $P(z,f)$ and $Q(z,f)$…

The existence of sufficiently many finite order meromorphic solutions of a differential equation, or difference equation, or differential-difference equation, appears to be a good indicator of integrability. In this paper, we investigate…

We consider a family of solutions of $q-$difference Riccati equation, and prove the meromorphic solutions of $q-$difference Riccati equation and corresponding second order $q-$difference equation are concerning with $q-$gamma function. The…

We will consider first-order difference equations of the form \[ y(z+1) = \frac{\lambda y(z)+a_2(z)y(z)^2+\cdots+a_p(z)y(z)^p}{1 + b_1(z)y(z)+\cdots+b_q(z)y(z)^q}, \] where $\lambda\in\mathbb{C}\setminus\{0\}$ and the coefficients $a_j(z)$…

Let $P(z)=z^{n}+a_{n-2}z^{n-2}+\cdots+a_0$ be a nonconstant polynomial and $S(z)$ be a nonzero rational function and denote $h(z)=S(z)e^{P(z)}$. Let $\theta\in(0,\pi/2n)$ be a constant and $\varepsilon>0$ be a small constant. It is shown…

In this article, we focus on studying the differential-difference equation \[ f'(z) = a(z)f(z+1) + R(z, f(z)), \quad R(z, f(z)) = \frac{P(z, f(z))}{Q(z, f(z))}, \] where the two nonzero polynomials \( P(z, f(z)) \) and \( Q(z, f(z)) \) in…

In this article, we study the growth of meromorphic solutions of linear delay-differential equation of the form \begin{equation*} \sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}(z)f^{(j)}(z+c_{i})=F(z), \end{equation*}% where $A_{ij}(z)$ $(i=0,1,\ldots…

It is shown that the difference equation \begin{equation}\label{abseq} (\Delta f(z))^2=A(z)(f(z)f(z+1)-B(z)), \qquad\qquad (1) \end{equation} where $A(z)$ and $B(z)$ are meromorphic functions, possesses a continuous limit to the…

In this paper we investigate the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations with entire or meromorphic coefficients. We further extend and improve few results on the order of meromorphic…

In this paper, we consider the behaviour, when $q$ goes to $1$, of the set of a convenient basis of meromorphic solutions of a family of linear $q$-difference equations. In particular, we show that, under convenient assumptions, such basis…

For two meromorphic functions $ f $ and $ g $, the equation $ f^m+g^m=1 $ can be regarded as Fermat-type equations. Using Nevanlinna theory for meromorphic functions in several complex variables, the main purpose of this paper is to…

It is known that $G$-functions solutions of a linear differential equation of order 1 with coefficients in $\overline{\mathbb{Q}}(z)$, are algebraic (of a very precise form). No general result is known when the order is 2. In this paper, we…

In this paper we have studied the growth of meromorphic solutions of higher order homogeneous and non-homogeneous linear difference equations with entire and meromorphic coefficients. We have extended and improved some results of Zhou and…