The Separation of Zeros of Solutions of Higher Order Linear Differential Equations With Entire Coefficients

2012 ◽  
Vol 63 (3-4) ◽  
pp. 1365-1373 ◽  
Author(s):  
Abdullah Alotaibi ◽  
J. K. Langley
Keyword(s):  
Differential Equations ◽  
Higher Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Zeros Of Solutions ◽  
Linear Differential ◽  
Separation Of Zeros

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 Sturm's Theorem for Equations with Delayed Argument

1994 ◽  
Vol 1 (3) ◽  
pp. 267-276
Author(s):  
A. Domoshnitsky
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Delayed Argument ◽  
Zeros Of Solutions ◽  
Linear Differential ◽  
Separation Of Zeros

Abstract Sturm's type theorems on separation of zeros of solutions are proved for the second order linear differential equations with delayed argument.

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