scholarly journals Zeros of solutions of certain higher order linear differential equations

2010 ◽  
Vol 97 (2) ◽  
pp. 123-136 ◽  
Author(s):  
Hong-Yan Xu ◽  
Cai-Feng Yi
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Zeros Of Solutions ◽  
Linear Differential

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.

Sign in / Sign up

Export Citation Format

Share Document