Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Growth Properties of Solutions to Higher Order Complex Linear Differential Equations with Analytic Coefficients in the Annulus
Authors: Benharrat Belaidi
Keywords: linear differential equations, analytic solutions, annulus, hyper order
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Keywords: linear differential equations, analytic solutions, annulus, hyper order
Abstract
In this paper, by using the Nevanlinna value distribution theory of meromorphic functions on an annulus, we deal with the growth properties of solutions of the linear differential equation $% f^{\left( k\right) }+B_{k-1}\left( z\right) f^{\left( k-1\right) }+\cdots +B_{1}\left( z\right) f^{\prime }+B_{0}\left( z\right) f=0$, where $k\geq 2$ is an integer and $B_{k-1}\left( z\right) ,...,B_{1}\left( z\right) ,B_{0}\left( z\right) $ are analytic on an annulus. Under some conditions on the coefficients, we obtain some results concerning the estimates of the order and the hyper-order of solutions of the above equation. The results obtained extend and improve those of Wu and Xuan in \cite{wx}.Department of Mathematics, Laboratory of Pure and
Applied Mathematics, University of Mostaganem
(UMAB), B. P. 227 Mostaganem-(Algeria)
E-mail:
Applied Mathematics, University of Mostaganem
(UMAB), B. P. 227 Mostaganem-(Algeria)
E-mail:
DOI
https://doi.org/10.56415/basm.y2023.i2.p19Fulltext
– 0.17 Mb
Contents
- The Second Hankel Determinant for k-symmetrical Functions
- Relative Separation Axioms via Semi-Open Sets
- Growth Properties of Solutions to Higher Order Complex Linear Differential Equations with Analytic Coefficients in the Annulus
- On T-nilpotence of a matrix set
- On the Existence of Stationary Nash Equilibria for Mean Payoff Games on Graphs
- Global Asymptotic Stability of Generalized Homogeneous Dynamical Systems
- The linear Fredholm integral equations with functionals and parameters
- B-spline collocation method for solving Fredholm integral equations with discontinuous right-hand side
- On recursive 1-differentiability of the quasigroup prolongations
- Zero-Order Markov Processes with Multiple Final Sequences of States
