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- Benharrat Belaïdi
- J. Systems Science & Complexity
- 2007

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.

- KARIMA HAMANI, Benharrat Belaïdi
- 2011

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 relationship between solutions and their derivatives of the differential equation f (k) + A(z)f = 0, k ≥ 2, where A(z) is a transcendental meromorphic function with ρp(A) = ρ > 0 and meromorphic functions of finite iterated p−order.

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 article, we give sufficiently conditions for the solutions and the differential polynomials generated by second-order differential equations to have the same properties of growth and oscillation. Also answer to the question posed by Cao [6] for the second-order linear differential equations in the unit disc.

In this paper, we investigate the growth of solutions of higher order linear differential equations with analytic coefficients in the unit disc ∆ = {z ∈ C : |z| < 1}. We obtain four results which are similar to those in the complex plane.

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)

- Karima HAMANI, Benharrat Belaïdi
- 2010

In this 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 nonhomogeneous linear differential equations.

- Benharrat Belaïdi, Hari M. Srivastava, KARIMA HAMANI
- 2004

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)