The growth of solutions of non-homogeneous linear differential equations

2021 ◽  
Vol 44 (3) ◽  
Author(s):  
Dinesh Kumar ◽  
Manisha Saini
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
Homogeneous Linear ◽  
Growth Of Solutions

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.

scholarly journals On the complex oscillation for a class of homogeneous linear differential equations

2000 ◽  
Vol 43 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Gao Shi-An
Keyword(s):  
Differential Equations ◽  
Open Problem ◽  
Linear Differential Equations ◽  
Unique Case ◽  
Linearly Independent ◽  
Complex Oscillation ◽  
Linear Differential ◽  
Dominant Condition ◽  
Homogeneous Linear ◽  
Independent Zero

AbstractUsing a combined dominant condition, we obtain general results concerning the complex oscillation for a class of homogeneous linear differential equations w(k) + + … + A1w′ + (A0 + A)w = 0 with k ≥ 2, which has been investigated by many authors. In particular, we discover that there exists a unique case that possesses k linearly independent zero-free solutions for these equations, and we resolve an open problem and simultaneously answer a question of Bank.

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