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

In this paper, we investigate the relationship between small functions and differential polynomials g f (z) = d 2 f + d 1 f + d 0 f , where d 0 (z) , d 1 (z) , d 2 (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 ≡ 0 are… (More)

- Karima HAMANI, Benharrat BELAÏDI, K. Hamani
- 2011

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 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 order and the hyper-order of solutions of the linear differential equation

- Zinelaâbidine Latreuch, Benharrat Belaïdi, Abdallah El Farissi
- Periodica Mathematica Hungarica
- 2013

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.

In this paper, we give a complete answer to Problem 1 and a partial answer to Problem 2 posed by F. Qi in [2] and we propose an open problem. Acknowledgements: The authors would like to thank the referees for their helpful remarks and suggestions to improve the paper.

- 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.