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[p, q]-order of solutions of complex differential equations in a sector of the unit disc

Belaidi, Benharrat; Zemirni, Mohamed Amine (Annals of the University of Craiova-Mathematics and Computer Science Series, 2018-12-02)

In this article, we study the growth of solutions of linear complex differential equations by using the concept of [p, q]-order in a sector of the unit disc instead of the whole unit disc, and we obtain similar results as ...

Growth of Solutions of Complex Differential Equations in a Sector of the Unit Disc

Belaïdi, Benharrat (arXiv preprint arXiv:1904.02259, 2019-04-03)

In this paper, we deal with the growth of solutions of homogeneous linear complex differential equation by using the concept of lower [\textit {p, q}]-order and lower [\textit {p, q}]-type in a sector of the unit disc ...

On open problems of F. Qi

Belaidi, Benharrat; El Farissi, Abdallah; Latreuch, Zinelaâbidine (JIPAM, 2009)

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 ...

The fixed points and iterated order of some differential polynomials

Belaıdi, Benharrat (Comment. Math. Univ. Carolin, 2009)

This paper is devoted to considering the iterated order and the fixed points of some differential polynomials generated by solutions of the differential equation f''+ A1 (z) f'+ A0 (z) f= F, where A1 (z), A0 (z)(≡ 0), F ...

Some Results On the Complex Oscillation Theory Of Some Differential Polynomials

Belaıdi, Benharrat; El Farissi, Abdallah (Acta Universitatis Apulensis, 2010)

In this paper, we investigate the complex oscillation of the differential polynomial gf= d2f+ d1f+ d0f, where dj (j= 0, 1, 2) are meromorphic functions with finite iterated p− order not all equal to zero generated by ...

Complex Oscillation Theory of Differential Polynomials

Belaïdi, Benharrat; El Farissi, Abdallah (Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, 2011)

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 entire functions that are not all equal to zero with ρ(dj) ...

Results on Shared Values of Entire Functions and their Homogeneous Differential Polynomials

Belaıdi, Benharrat; Bouabdelli, Rabab (International Journal of Difference Equations, 2013)

The present paper introduces various results for studying the uniqueness of entire functions and the linear combination of its derivatives L[f] sharing one value and two small entire functions. The results improve some ...

Nonexistence of subnormal solutions for a class of higher order complex differential equations

Belaïdi, Benharrat; Zemirni, Mohamed Amine (Bulletin of the Transilvania University of Brasov. Mathematics, Informatics, Physics. Series III, 2015-07-01)

In this article, we investigate the existence of subnormal solutions for a class of higher order complex di erential equations. We generalize the result of N. Li and L. Z. Yang [14], L. P. Xiao [17] and also result of ...

The growth of solutions of some linear differential equations with coefficients being Lacunary series of (p, q)-order

Belaidi, Benharrat; Ferraoun, Amina (Facta Universitatis, Series: Mathematics and Informatics, 2015-12-09)

In this paper, we study the growth of meromorphic solutions of certain linear differential equations with entire coefficients being Lacunary series. We extend some previous results due to L. M. Li and T. B. Cao [9] and ...

On the growth of solutions of some non-homogeneous linear differential equations

Belaidi, Benharrat; Habib, Habib (Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, 2016)

In this paper, we investigate the growth of solutions to the non-homogeneous linear di erential equation f(k) + Ak􀀀1ebk􀀀1zf(k􀀀1) + + A1eb1zf 0 + A0eb0zf = Feaz; where Aj(z) 6 0 (j = 0; 1; : : : ; k 􀀀 1), ...

On the (p, q)-order of solutions of some complex linear differential equations

BELAIDI, BENHARRAT; FERRAOUN, AMINA (Communications in Optimization Theory, 2017)

In this paper, we study the growth of solutions of some complex linear differential equations and we obtain some results on the (p, q)-order of these solutions. The results presented in this paper mainly improve the ...

On the hyper-order of transcendental meromorphic solutions of certain higher order linear differential equations

Belaïdi, Benharrat; Hamani, Karima (Opuscula Mathematica, 2017)

In this paper, we investigate the growth of meromorphic solutions of the linear differential equation f (k) + hk−1(z)ePk−1(z) f (k−1) + . . . + h0(z)eP0(z) f = 0, where k 2 is an integer, Pj(z) (j = 0, 1, . . . , ...

Complex Oscillation of Differential Polynomials Generated by Meromorphic Solutions of [p, q] Order to Complex Non-homogeneous Linear Differential Equations

Belaıdi, Benharrat; Abdellaoui, Mohammed Amin (J. Math. Study, 2017-03)

In this article we study the complex oscillation of differential polynomials generated by meromorphic solutions of the non-homogeneous linear differential equation f (k)+ Ak− 1 (z) f (k− 1)+···+ A1 (z) f′+ A0 (z) f= F, ...

Growth of solutions of certain non-homogeneous linear differential equations with entire coefficients

Belaidi, Benharrat (J. Ineq. Pure Appl. Math.(2), 2004)

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 ...

Some properties of solutions of certain complex linear differential equations with meromorphic doefficients

Belaïdi, Benharrat; El Farissi, Abdallah (Methods and Applications of Analysis, 2007)

In this paper, we investigate the relationship between the solutions, their 1st and 2nd derivatives of some second order linear differential equations and meromorphic function of finite order. We obtain some precise estimates.

Differential polynomials generated by second order linear differential equations

Belaïdi, Benharrat; El Farissi, Abdallah (Journal of Applied Analysis, 2008)

In this paper, we study fixed points of solutions of the differential equation f+ A1 (z) f+ A0 (z) f= 0, where Aj (z)(≡ 0)(j= 0, 1) are transcendental meromorphic functions with finite order. Instead of looking at the zeros ...

Relation between differential polynomials of certain complex linear differential equations and meromorphic functions of finite order

Belaïdi, Benharrat; El Farissi, Abdallah (Tsukuba Journal of Mathematics, 2008)

In this paper, we investigate the relationship between di¤erential polynomials and meromorphic functions of finite order of some second order linear di¤erential equations with meromorphic coe‰cients. We obtain some ...

Growth and oscillation theories of differential polynomials

Belaıdi, Benharrat; El Farissi, Abdallah (Novi Sad J. Math, 2009)

In this paper we investigate the complex oscillation and the growth of some differential polynomials generated by the solutions of the differential equation f''+ A1 (z) f'+ A0 (z) f= F, where A1 (z), A0 (z)(≡ 0), F are ...

On the growth of solutions of some higher order linear differential equations

Belaïdi, Benharrat; El Farissi, Abdallah (Applications of Mathematics, 2012-08-01)

n this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation f (k)+ Ak− 1f (k− 1)+...+ A2f′′+(D1 (z)+ A1 (z) eaz) f′+(D0 (z)+ A0 (z) ebz) f= F (k⩾ 2), where a, b are complex ...

Growth and oscillation related to a second order linear differential equation

Belaϊdi, Benharrat (Mathematical Communications, 2013-05-10)

This paper is devoted to studying the growth and the oscillation of solutions of the second order non-homogeneous linear di erential equation f00 + A1 (z) eP(z)f0 + A0 (z) eQ(z)f = F; where P (z), Q(z) are nonconstant ...

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