Growth and oscillation theory of solutions of some linear differential equations

Abstract

The basic idea of this paper is to considerfixed 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 atranscendental meromorphic function with $\rho \left( A\right) =\rho >0$.Instead of looking at the zeros of $f\left( z\right) -z$, we proceed to aslight generalization by considering zeros of $f\left( z\right) -\varphi\left( z\right) $, where $\varphi $ is a meromorphic function of finiteorder, while the solution of respective differential equation is of infiniteorder.