Oscillation of solutions and their arbitrary order derivatives of higher order non-homogeneous LDE

Abstract

In this paper, we investigate the iterated order of solutions of higher order nonhomogeneous linear differential equations Ak (z) f (k)+Ak􀀀1 (z) f (k􀀀1)+ +A1 (z) f ′ +A0 (z) f = F (z) ; where A0 (z) ;A1 (z) ; ;Ak (z) ̸ 0 are entire functions of finite iterated p􀀀order and F (z) is entire function of infinite iterated p􀀀order. We improve and extend some recent results of Chen and we obtain general estimates of the iterated convergence exponent, the iterated p-order and the iterated convergence exponent of arbitrary order derivatives of the solutions of the above equation.