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

摘要

In this paper, we investigate the relationship between solutions and theirderivatives of the differential equation f(k) + Af = 0 for k 2 and meromorphicfunctions of infinite iterated p-order, where A is a meromorphic function of finiteiterated p-order Pp (A) = P. We also study the oscillation theory of derivatives of thenonhomogeneous 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.