scholarly journals Differential polynomials generated by some complex linear differential equations with meromorphic coefficients

2008 ◽  
Vol 43 (2) ◽  
pp. 363-373 ◽  
Author(s):  
Benharrat Belaidi
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Differential Polynomials ◽  
Complex Linear ◽  
Linear Differential

scholarly journals On [p,q]-order of growth of solutions of complex linear differential equations near a singular point

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4013-4020
Author(s):  
Jianren Long ◽  
Sangui Zeng
Keyword(s):  
Differential Equation ◽  
Singular Point ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Linear Differential Equations ◽  
Order Of Growth ◽  
Complex Linear ◽  
Linear Differential ◽  
Growth Of Solutions

We investigate the [p,q]-order of growth of solutions of the following complex linear differential equation f(k)+Ak-1(z) f(k-1) + ...+ A1(z) f? + A0(z) f = 0, where Aj(z) are analytic in C? - {z0}, z0 ? C. Some estimations of [p,q]-order of growth of solutions of the equation are obtained, which is generalization of previous results from Fettouch-Hamouda.

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.

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