Journal of Applied Analysis 14 (2008), No. 2, 259--271
Copyright Heldermann Verlag 2008
Differential Polynomials Generated by Second Order Linear Differential Equations
Benharrat Belaïdi
Dept. of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem, B. P. 227, Mostaganem, Algeria
belaidi@univ-mosta.dz
Abdallah El Farissi
Dept. of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem, B. P. 227, Mostaganem, Algeria
el.farissi.abdallah@caramail.com
[Abstract-pdf]
We study fixed points of solutions of the differential equation \begin{equation*} f^{{\prime \prime }}+A_{1}\left( z\right) f^{{\prime }}+A_{0}\left(z\right) f=0, \end{equation*} where $A_{j}\left( z\right) $ $\left( \not\equiv 0\right)$ $\left( j=0, 1 \right)$ are transcendental meromorphic functions with finite order. Instead of looking at the zeros of $f\left( z\right)-z$, we proceed to a slight generalization by considering zeros of $g\left(z\right)-\varphi \left( z\right)$, where $g$ is a differential polynomial in $f$ with polynomial coefficients, $\varphi$ is a small meromorphic function relative to $f$, while the solution $f$ is of infinite order.
Keywords: Linear differential equations, meromorphic solutions, hyper order, exponent of convergence of the sequence of distinct zeros, hyper exponent of convergence of the sequence of distinct zeros.
MSC: 34M10, 30D35
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