On the Growth of Solutions of Some Second Order Linear Differential Equations with Entire Coefficients

Belaïdi, Benharrat; Habib, Habib

doi:10.2478/auom-2013-0022

Abstract

In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation where n≥2 is an integer, Aj (z) (≢0) (j = 1,2) are entire functions with max {σ A(j) : (j = 1,2} < 1, Q (z) = q_mz^m + ... + q₁z + q₀ is a nonoonstant polynomial and a₁, a₂ are complex numbers. Under some conditions, we prove that every solution f (z) ≢ 0 of the above equation is of infinite order and hyper-order 1.

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On the Growth of Solutions of Some Second Order Linear Differential Equations with Entire Coefficients

Abstract

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