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2017•Opuscula MathematicaOpen access

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

Karima Hamani, Benharrat Belaïdi

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Abstract

In this paper, we investigate the growth of meromorphic solutions of the linear differential equationwhere k ≥ 2 is an integer, Pj(z) (j = 0, 1, . . ., k -1) are nonconstant polynomials and hj(z) are meromorphic functions.Under some conditions, we determine the hyper-order of these solutions.We also consider nonhomogeneous linear differential equations.

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In this paper, we investigate the growth of meromorphic solutions of the linear differential equationwhere k ≥ 2 is an integer, Pj(z) (j = 0, 1, . . ., k -1) are nonconstant polynomials and hj(z) are meromorphic functions.Under some conditions, we determine the hyper-order of these solutions.We also consider nonhomogeneous linear differential equations.

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Available abstract

In this paper, we investigate the growth of meromorphic solutions of the linear differential equationwhere k ≥ 2 is an integer, Pj(z) (j = 0, 1, . . ., k -1) are nonconstant polynomials and hj(z) are meromorphic functions.Under some conditions, we determine the hyper-order of these solutions.We also consider nonhomogeneous linear differential equations.

Key concepts: Meromorphic function, Mathematics, Transcendental number, Order (exchange), Applied mathematics, Mathematical analysis, Differential equation, Pure mathematics

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