scholarly journals Relation between small functions with differential polynomials generated by meromorphic solutions of higher order linear differential equations

2014 ◽  
Vol 38 (1) ◽  
pp. 147-161
Author(s):  
Benharrat Belaïdi ◽  
Zinelâabidine Latreuch
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Differential Polynomials ◽  
Meromorphic Solutions ◽  
Order Linear ◽  
Small Functions ◽  
Linear Differential

scholarly journals On the growth and the zeros of solutions of higher order linear differential equations with meromorphic coefficients

2015 ◽  
Vol 98 (112) ◽  
pp. 199-210
Author(s):  
Maamar Andasmas ◽  
Benharrat Belaïdi
Keyword(s):  
Differential Equations ◽  
Infinite Order ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Meromorphic Solutions ◽  
Exponent Of Convergence ◽  
Order Linear ◽  
Zeros Of Solutions ◽  
Hyper Order ◽  
Linear Differential

We investigate the growth of meromorphic solutions of homogeneous and nonhomogeneous higher order linear differential equations f(k) + k-1?j=1 Ajf(j) + A0f = 0 (k ? 2); f(k) + k-1 ?j=1 Ajf(j) + A0f = Ak (k ? 2); where Aj(z)(j=0,1,...,k) are meromorphic functions with finite order. Under some conditions on the coefficients, we show that all meromorphic solutions f ?/0 of the above equations have an infinite order and infinite lower order. Furthermore, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros. We improve the results due to Kwon, Chen and Yang, Bela?di, Chen, Shen and Xu.

scholarly journals Some Properties on The [p,q]-Order of Meromorphic Solutions of Homogeneous and Non-homogeneous Linear Differential Equations With Meromorphic Coefficients

2021 ◽  
Vol 1 (2) ◽  
pp. 86-105
Author(s):  
Mansouria Saidani ◽  
Benharrat Belaidi
Keyword(s):  
Differential Equations ◽  
Meromorphic Functions ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Meromorphic Solutions ◽  
Order Linear ◽  
Linear Differential ◽  
Right Order ◽  
Homogeneous Linear

In the present paper, we investigate the $\left[p,q\right] $-order of solutions of higher order linear differential equations \begin{equation*} A_{k}\left(z\right) f^{\left( k\right) }+A_{k-1}\left( z\right) f^{\left(k-1\right)}+\cdots +A_{1}\left( z\right) f^{\prime }+A_{0}\left( z\right)   f=0 \end{equation*} and \begin{equation*} A_{k}\left( z\right) f^{\left( k\right) }+A_{k-1}\left( z\right) f^{\left(k-1\right) }+\cdots +A_{1}\left( z\right) f^{\prime }+A_{0}\left( z\right) f=F\left( z\right), \end{equation*} where $A_{0}\left( z\right) ,$ $A_{1}\left( z\right) ,...,A_{k}\left(z\right) \not\equiv 0$ and $F\left( z\right) \not\equiv 0$ are meromorphic functions of finite $\left[ p,q\right] $-order. We improve and extend some results of the authors by using the concept $\left[ p,q\right] $-order.

scholarly journals Some Oscillation Results of Higher-Order Linear Differential Equations with Meromorphic Coefficients

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Zhigang Huang
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Small Functions ◽  
Linear Differential ◽  
The Relationship ◽  
Growth Of Solutions

We investigate the growth of solutions of higher-order nonhomogeneous linear differential equations with meromorphic coefficients. We also discuss the relationship between small functions and solutions of such equations.

scholarly journals On the Iterated Exponent of Convergence of Solutions of Linear Differential Equations with Entire and Meromorphic Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Rabab Bouabdelli ◽  
Benharrat Belaïdi
Keyword(s):  
Differential Equations ◽  
Meromorphic Functions ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Exponent Of Convergence ◽  
Order Linear ◽  
Convergence Of Solutions ◽  
Small Functions ◽  
The Difference ◽  
Linear Differential

We investigate the zeros of the difference of the derivative of solutions of the higher-order linear differential equationsf(k)+Ak-1(z)f(k-1)+⋯+A1(z)f′+A0(z)f=0and small functions, whereA0(z),…,Ak-1(z)are entire or meromorphic functions of finite iteratedporder.

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