scholarly journals Complex oscillation of differential polynomials generated by meromorphic solutions of linear differential equations

2011 ◽  
Vol 90 (104) ◽  
pp. 125-133
Author(s):  
Benharrat Belaïdi
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Meromorphic Functions ◽  
Linear Differential Equations ◽  
Differential Polynomials ◽  
Meromorphic Solutions ◽  
Complex Oscillation ◽  
Linear Differential

We investigate the complex oscillation of some differential polynomials generated by solutions of the differential equation f'' + A1(z)f' + A0(z)f = 0, where A1(z), A0(z) are meromorphic functions having the same finite iterated p-order.

scholarly journals Relation between Small Functions with Differential Polynomials Generated by Solutions of Linear Differential Equations

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

This paper is devoted to studying the growth of solutions of second-order nonhomogeneous linear differential equation with meromorphic coefficients. We also discuss the relationship between small functions and differential polynomialsL(f)=d2f″+d1f′+d0fgenerated by solutions of the above equation, whered0(z),d1(z),andd2(z)are entire functions that are not all equal to zero.

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 On the Complex Oscillation of Meromorphic Solutions of Nonhomogeneous Linear Differential Equations with Meromorphic Coefficients

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Chuang-Xin Chen ◽  
Ning Cui ◽  
Zong-Xuan Chen
Keyword(s):  
Differential Equation ◽  
Meromorphic Function ◽  
Differential Equations ◽  
Rational Function ◽  
Finite Order ◽  
Order Differential Equation ◽  
Higher Order ◽  
Meromorphic Solutions ◽  
Complex Oscillation ◽  
Linear Differential

In this paper, we study the higher order differential equation f k + B f = H , where B is a rational function, having a pole at ∞ of order n > 0 , and H ≡ 0 is a meromorphic function with finite order, and obtain some properties related to the order and zeros of its meromorphic solutions.

A mechanical method for the solution of second-order linear differential equations

1931 ◽  
Vol 27 (4) ◽  
pp. 546-552 ◽  
Author(s):  
E. C. Bullard ◽  
P. B. Moon
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Order Differential Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Mechanical Method ◽  
Order Linear ◽  
Second Order Differential Equation ◽  
Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

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