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In the present paper, we investigate the iterated order of solutions of higher order homogeneous linear differential equations with entire coefficients. We improve and extend some results of Bela¨ıdi and Hamouda by using the concept of the iterated order. We also consider the non-homogeneous linear differential equations. 1.Introduction and main results In(More)
In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation f + Q e −z f + (A1e a 1 z + A2e a 2 z) n f = 0, where n 2 is an integer, Aj (z) (≡ 0) (j = 1, 2) are entire functions with max {σ (Aj) : j = 1, 2} < 1, Q (z) = qmz m + · · · + q1z + q0 is a nonconstant polynomial and a1, a2 are complex(More)
In this paper, we investigate the growth of solutions of the differential equation f (k) + A k−1 (z) f (k−1) + · · · + A 1 (z) f + A 0 (z) f = F, where A 0 (z) ,. .. , A k−1 (z) , F (z) / ≡ 0 are entire functions, and we obtain general estimates of the hyper-exponent of convergence of distinct zeros and the hyper-order of solutions for the above equation.