Oscillation and fixed points of derivatives of solutions of some linear differential equations

Abstract

In this paper, we investigate the relationship between solutions and their derivatives of the differential equation f(k) + Af = 0 for k > 2 and meromorphic functions of infinite iterated p-order, where A is a meromorphic function of finite iterated p-order Pp (A) = P. We also study the oscillation theory of derivatives of the nonhomogeneous differential equation f(k) + Af = F for k > 2. Keywords: linear differential equations, meromorphic solutions, iterated p-order, iterated exponent of convergence of the sequence of distinct zeros. 2010 Mathematics Subject Classification: 34M10, 30D35.