Searcharxiv⌕ Search

arXiv subjects

Benharrat Belaïdi

Publications and source records attributed to Benharrat Belaïdi.

9 recordsLinked to original sources
arXiv2025

Growth of (α,\b{eta},γ)-order solutions of linear differential equations with analytic coefficients in the unit disc

In this paper, we study the growth of solutions to higher-order complex linear differential equations in the unit disc, where the analytic coefficients are of finite (α,\b{eta},γ)-order. By employing the concepts of (α,\b{eta},γ)-order and (α,\b{eta},γ)-type, we establish new results concerning the growth of such solutions. These results extend and generalize previous work by the second author and by Biswas.

math.CV↗
arXiv2024

Growth estimates of solutions of linear differential equations with dominant coefficient of lower $(α,β,γ)$-order

In this paper, we deal with the growth and oscillation of solutions of higher order linear differential equations. Under the conditions that there exists a coefficient which dominates the other coefficients by its lower $% (α,β,γ)$-order and lower $(α,β,γ)$-type, we obtain some growth and oscillation properties of solutions of such equations which improve and extend some recently results of the author and Biswas \cite{b8}.

math.CV↗
arXiv2024

On The Relationship Between The Logarithmic Lower Order of Coefficients and The Growth of Solutions of Complex Linear Differential Equations in $\overline{\mathbb{C}}\setminus\{z_{0}\}$

In this article, we study the growth of solutions of the homogeneous complex linear differential equation \begin{equation*} f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f^{\prime}+ A_{0}(z)f=0, \end{equation*}% where the coefficients $A_{j}(z)$ $(j=0,1,\ldots ,k-1)$ are analytic or meromorphic functions in $\overline{\mathbb{C}}\setminus\{z_{0}\}$. Under the sufficient condition that there exists one dominant coefficient by its logarithmic lower order or by its logarithmic lower type. We extend some precedent results due to Liu, Long and Zeng and others.

math.CV↗
arXiv2022

Finite Logarithmic Order Meromorphic Solutions of Complex Linear Delay-Differential Equations

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 $A_{ij}(z)$ $(i=0,1,\ldots ,n,j=0,1,\ldots ,m,n,m\in \mathbb{N})$ and $% F(z)$ are meromorphic of finite logarithmic order, $c_{i}(i=0,\ldots ,n)$ are distinct non-zero complex constants. We extend those results obtained recently by Chen and Zheng, Bellaama and Bela\"ıdi to the logarithmic lower order.

math.CV↗
arXiv2021

Lower Bound Estimates of the Order of Meromorphic Solutions to Non-Homogeneous Linear Differential-Difference Equations

In this article, we deal with the order of growth of solutions of non-homogeneous linear differential-difference equation \begin{equation*} \sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=F(z), \end{equation*} where $A_{ij},$ $F\left( z\right) $ are entire or meromorphic functions and $c_{i}$ $\left( 0,1,...,n\right) $ are non-zero distinct complex numbers. Under the sufficient condition that there exists one coefficient having the maximal lower order or having the maximal lower type strictly greater than the order or the type of other coefficients, we obtain estimates of the lower bound of the order of meromorphic solutions of the above equation.

math.CV↗