scholarly journals On the growth of solutions of certain linear differential equations

1992 ◽  
Vol 17 ◽  
pp. 343-365 ◽  
Author(s):  
Simon Hellerstein ◽  
Joseph Miles ◽  
John Rossi
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Linear Differential ◽  
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.

LOCALISATION OF LINEAR DIFFERENTIAL EQUATIONS IN THE UNIT DISC BY A CONFORMAL MAP

2015 ◽  
Vol 93 (2) ◽  
pp. 260-271
Author(s):  
JUHA-MATTI HUUSKO
Keyword(s):  
Differential Equations ◽  
Lower Bounds ◽  
Complex Plane ◽  
Exponential Growth ◽  
Unit Disc ◽  
Linear Differential Equations ◽  
Conformal Map ◽  
Conformal Maps ◽  
Linear Differential ◽  
Growth Of Solutions

We obtain lower bounds for the growth of solutions of higher order linear differential equations, with coefficients analytic in the unit disc of the complex plane, by localising the equations via conformal maps and applying known results for the unit disc. As an example, we study equations in which the coefficients have a certain explicit exponential growth at one point on the boundary of the unit disc and consider the iterated $M$-order of solutions.

DIFFERENTIAL EQUATIONS WITH COEFFICIENTS OF SLOW GROWTH IN THE UNIT DISC

2009 ◽  
Vol 07 (02) ◽  
pp. 213-224 ◽  
Author(s):  
LIPENG XIAO ◽  
ZONGXUAN CHEN
Keyword(s):  
Differential Equations ◽  
Recent Result ◽  
Unit Disc ◽  
Slow Growth ◽  
Linear Differential Equations ◽  
Fast Growing ◽  
Linearly Independent ◽  
Linear Differential ◽  
Growth Of Solutions

In this paper, the growth of solutions and the number of fast-growing linearly independent solutions of certain linear differential equations with coefficients of slow growth in the unit disc are investigated. The results we obtain are a generalization of a recent result due to Korhonen and Rättyä.

scholarly journals Complex Oscillation of Higher-Order Linear Differential Equations with Coefficients Being Lacunary Series of Finite Iterated Order

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Jin Tu ◽  
Hong-Yan Xu ◽  
Hua-ming Liu ◽  
Yong Liu
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Lacunary Series ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Iterated Order ◽  
Complex Oscillation ◽  
Linear Differential ◽  
Growth Of Solutions

The authors introduce the lacunary series of finite iterated order and use them to investigate the growth of solutions of higher-order linear differential equations with entire coefficients of finite iterated order and obtain some results which improve and extend some previous results of Belaidi, 2006, Cao and Yi, 2007, Kinnunen, 1998, Laine and Wu, 2000, Tu and Chen, 2009, Tu and Deng, 2008, Tu and Deng, 2010, Tu and Liu, 2009, and Tu and Long, 2009.

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