MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Growth and oscillation theory of solutions of some linear differential equations
Benharrat Bela\"\i di Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of Mostaganem, B. P 227 Mostaganem--(Algeria), E-mail: belaidi

Abstract

The basic idea of this paper is to consider fixed points of solutions of the differential equation $f^{\left( k\right) }+A\left( z\right) f=0$, $k\geq 2$, where $A\left( z\right) $ is a transcendental meromorphic function with $\rho \left( A\right) =\rho >0$. Instead of looking at the zeros of $f\left( z\right) -z$, we proceed to a slight generalization by considering zeros of $f\left( z\right) -\varphi \left( z\right) $, where $\varphi $ is a meromorphic function of finite order, while the solution of respective differential equation is of infinite order.

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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

Pages:  233--246     

Volume  60 ,  Issue  4 ,  2008