Benharrat Belaïdi

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In this paper, we investigate the growth of solutions of the differential equation f (k) +Ak−1 (z) f (k−1) + · · ·+A1 (z) f ′ +A0 (z) f = F, where A0 (z) , . . . , Ak−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.
Abstract. In this paper, we investigate the growth of solutions of higher order homogeneous linear differential equations with entire coefficients. We improve and extend the results of Beläıdi and Hamouda by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen and the Wiman-Valiron theory. We also(More)
In this paper, we investigate the order and the hyper order of entire solutions of the higher order linear differential equation f +Ak−1 (z) e k−1f +...+A1 (z) e 1f ′ +A0 (z) e 0f = 0 (k ≥ 2) , where Pj (z) (j = 0, ..., k − 1) are nonconstant polynomials such that degPj = n (j = 0, ..., k − 1) and Aj (z) ( ≡ 0) (j = 0, ..., k − 1) are entire functions with(More)
In this paper, we investigate the relationship between small functions and differential polynomials gf (z) = d2f ′′ + d1f ′ + d0f , where d0 (z) , d1 (z) , d2 (z) are meromorphic functions that are not all equal to zero with finite order generated by solutions of the second order linear differential equation f ′′ + Af ′ +Bf = F, where A, B, F 6≡ 0 are(More)
In this paper, we study the possible orders of transcendental solutions of the differential equation f (n) + an−1 (z) f (n−1) + · · · + a1 (z) f ′ + a0 (z) f = 0, where a0 (z) , . . . , an−1 (z) are nonconstant polynomials. We also investigate the possible orders and exponents of convergence of distinct zeros of solutions of non-homogeneous differential(More)