On the Comparison of One Pair of Second Order Linear Differential Equations

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J. Math. Sci. Univ. Tokyo
Vol. 20 (2013), No. 3, Page 317–333.

LATREUCH, Zinelâabidine ; BELAïDI, Benharrat
On the Comparison of One Pair of Second Order Linear Differential Equations
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
The main purpose of this paper is to study the controllability of solutions of one pair of linear differential equations

$\begin{equation*} f^{\prime \prime }+A\left( z\right) f=0 \end{equation*}$ and

$\begin{equation*} g^{\prime \prime }+B\left( z\right) g=0. \end{equation*}$ We study the growth and oscillation of

$w=d_{1}f+d_{2}g,$ where

$f,g$ are the solutions of the above equations and

$d_{1},d_{2}$ are entire functions of finite order.

Keywords: Linear differential equations, Order of growth, Hyper-order, Exponent of convergence of the sequence of distinct zeros, Hyper-exponent of convergence of the sequence of distinct zeros.

Mathematics Subject Classification (2010): 34M10, 30D35.

Mathematical Reviews Number: MR3156984

Received: 2013-01-21

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