scholarly journals On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jianren Long ◽  
Chunhui Qiu ◽  
Pengcheng Wu
Keyword(s):  
Lower Bound ◽  
Differential Equations ◽  
Infinite Order ◽  
Entire Functions ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential ◽  
Growth Of Solutions

We consider that the linear differential equationsf(k)+Ak-1(z)f(k-1)+⋯+A1(z)f′+A0(z)f=0, whereAj  (j=0,1,…,k-1), are entire functions. Assume that there existsl∈{1,2,…,k-1}, such thatAlis extremal forYang'sinequality; then we will give some conditions on other coefficients which can guarantee that every solutionf(≢0)of the equation is of infinite order. More specifically, we estimate the lower bound of hyperorder offif every solutionf(≢0)of the equation is of infinite order.

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.

scholarly journals On the growth and the zeros of solutions of higher order linear differential equations with meromorphic coefficients

2015 ◽  
Vol 98 (112) ◽  
pp. 199-210
Author(s):  
Maamar Andasmas ◽  
Benharrat Belaïdi
Keyword(s):  
Differential Equations ◽  
Infinite Order ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Meromorphic Solutions ◽  
Exponent Of Convergence ◽  
Order Linear ◽  
Zeros Of Solutions ◽  
Hyper Order ◽  
Linear Differential

We investigate the growth of meromorphic solutions of homogeneous and nonhomogeneous higher order linear differential equations f(k) + k-1?j=1 Ajf(j) + A0f = 0 (k ? 2); f(k) + k-1 ?j=1 Ajf(j) + A0f = Ak (k ? 2); where Aj(z)(j=0,1,...,k) are meromorphic functions with finite order. Under some conditions on the coefficients, we show that all meromorphic solutions f ?/0 of the above equations have an infinite order and infinite lower order. Furthermore, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros. We improve the results due to Kwon, Chen and Yang, Bela?di, Chen, Shen and Xu.

scholarly journals Some Oscillation Results of Higher-Order Linear Differential Equations with Meromorphic Coefficients

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

We investigate the growth of solutions of higher-order nonhomogeneous linear differential equations with meromorphic coefficients. We also discuss the relationship between small functions and solutions of such equations.

scholarly journals GROWTH OF \(\varphi\)–ORDER SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS ON THE COMPLEX PLANE

2020 ◽  
Vol 6 (1) ◽  
pp. 95
Author(s):  
Mohamed Abdelhak Kara ◽  
Benharrat Belaïdi
Keyword(s):  
Differential Equations ◽  
Complex Plane ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential ◽  
Growth Of Solutions

In this paper, we study the growth of solutions of higher order linear differential equations with meromorphic coefficients of \(\varphi\)-order on the complex plane. By considering the concepts of \(\varphi\)-order and \(\varphi \)-type, we will extend and improve many previous results due to Chyzhykov–Semochko, Belaïdi, Cao–Xu–Chen, Kinnunen.

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