On the complex zeros of solutions of linear differential equations

1992 ◽  
Vol 161 (1) ◽  
pp. 83-112 ◽  
Author(s):  
Steven B. Bank
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Zeros Of Solutions ◽  
Linear Differential ◽  
Complex 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 Distributions of Zeros of Solutions for Third-Order Differential Equations with Variable Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Samir H. Saker ◽  
Mohammed A. Arahet
Keyword(s):  
Differential Equations ◽  
Lower Bounds ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
The Third ◽  
Hardy's Inequality ◽  
Zeros Of Solutions ◽  
Linear Differential

For the third-order linear differential equations of the formr(t)x′′(t)′+p(t)x′(t)+q(t)x(t)=0, we will establish lower bounds for the distance between zeros of a solution and/or its derivatives. The main results will be proved by making use of Hardy’s inequality and some generalizations of Opial and Wirtinger type inequalities.

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