scholarly journals A bound for zeros of solutions to a higher order non-homogeneous ODE with polynomial coefficients

2021 ◽  
pp. 405-416
Author(s):  
M. I. Gil'
Keyword(s):  
Higher Order ◽  
Polynomial Coefficients ◽  
Zeros Of Solutions

scholarly journals Bounds for Products of Zeros of Solutions to Nonhomogeneous ODE with Polynomial Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Michael Gil’
Keyword(s):  
Entire Function ◽  
Counting Function ◽  
Polynomial Coefficients ◽  
Zeros Of Solutions ◽  
Free Domain

We consider the equationu″=P(z)u+F(z)  (z∈C), whereP(z)is a polynomial andF(z)is an entire function. Letzk(u)  (k=1,2,…)be the zeros of a solutionu(z)to that equation. Lower estimates for the products∏k=1j|zk(u)|  (j=1,2,…)are derived. In particular, they give us a bound for the zero free domain. Applications of the obtained estimates to the counting function of the zeros of solutions are also discussed.

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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