scholarly journals Complex linear differential equations with certain analytic coefficients of [ p , q ] -order in the unit disc

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Jin Tu ◽  
Zu-Xing Xuan
Keyword(s):  
Differential Equations ◽  
Unit Disc ◽  
Linear Differential Equations ◽  
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.

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.

Sign in / Sign up

Export Citation Format

Share Document