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In this paper, we investigate the iterated order of solutions of higher order nonhomogeneous linear differential equations Ak (z) f +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.

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