scholarly journals Overconvergence Phenomena and Grouping in Exponential Representation of Solutions of Linear Differential Equations of Infinite Order

2001 ◽  
Vol 161 (2) ◽  
pp. 131-140 ◽  
Author(s):  
Takahiro Kawai ◽  
Daniele C. Struppa
Keyword(s):  
Differential Equations ◽  
Infinite Order ◽  
Linear Differential Equations ◽  
Representation Of Solutions ◽  
Linear Differential

scholarly journals Linear differential equations of infinite order and theta functions

1983 ◽  
Vol 47 (3) ◽  
pp. 300-325 ◽  
Author(s):  
Mikio Sato ◽  
Masaki Kashiwara ◽  
Takahiro Kawai
Keyword(s):  
Differential Equations ◽  
Infinite Order ◽  
Theta Functions ◽  
Linear Differential Equations ◽  
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.

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