publication . Article . Other literature type . 2002

Growth of solutions of an n-th order linear differential equation with entire coefficients

Bela\"{i}di, Benharrat; Hamouda, Saada;
Restricted
  • Published: 01 Oct 2002 Journal: Kodai Mathematical Journal, volume 25, pages 240-245 (issn: 0386-5991, Copyright policy)
  • Publisher: Tokyo Institute of Technology, Department of Mathematics
Abstract
We consider a differential equation $f^{\left( n\right) }+A_{n-1}\left( z\right) f^{\left( n-1\right) }+...+A_{1}\left( z\right) f^{^{/}}+A_{0}\left( z\right) f=0,$ where $A_{0}\left( z\right) ,...,A_{n-1}\left( z\right) $ are entire functions with $A_{0}\left( z\right) \hbox{$/\hskip -11pt\equiv$}0$. Suppose that there exist a positive number $\mu ,$\ and a sequence $\left( z_{j}\right) _{j\in N}$ with $\stackunder{j\rightarrow +\infty }{\lim }z_{j}=\infty ,$ \ and also two real numbers $\alpha ,\beta $ $\left( \ 0\leq \beta \alpha \right) $\ such that \ $\left| A_{0}\left( z_{j}\right) \right| \geq e^{\alpha \left| z_{j}\right| ^{\mu }}\quad $and$% \quad \left...
Subjects
free text keywords: General Mathematics, Mathematical analysis, Homogeneous differential equation, Mathematics, Universal differential equation, Matrix differential equation, Hill differential equation, symbols.namesake, symbols, Differential equation, First-order partial differential equation, Characteristic equation, Linear differential equation
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publication . Article . Other literature type . 2002

Growth of solutions of an n-th order linear differential equation with entire coefficients

Bela\"{i}di, Benharrat; Hamouda, Saada;