A Remark on Distribution of Zeros of Solutions of Linear Differential Equations

1995 ◽  
Vol 123 (3) ◽  
pp. 847
Author(s):  
Zheng Jian Hua
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Distribution Of Zeros ◽  
Zeros Of Solutions ◽  
Linear Differential

scholarly journals The distribution of zeros of solutions for a class of third order differential equation

2021 ◽  
Vol 40 (5) ◽  
pp. 1301-1321
Author(s):  
Clemente Cesarano ◽  
Mohammed A. Arahet ◽  
Tareq M. Al-Shami
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Lower Bounds ◽  
Order Differential Equation ◽  
Linear Differential Equations ◽  
Distribution Of Zeros ◽  
Third Order ◽  
Order Linear ◽  
Zeros Of Solutions ◽  
Linear Differential

For third order linear differential equations of the form r(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 Hardyís inequality, some generalizations of Opialís inequality and Boydís inequality.

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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