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Fast Growing Solutions to Linear Differential Equations with Entire Coefficients Having the Same ρ ϕ -order

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Fast Growing Solutions to Linear Differential Equations with Entire Coefficients Having the Same ρ ϕ -order

Benharrat Bela¨ıdi

Abstract: This paper deals with the growth of solutions of a class of higher order linear differential equations

f(k)+ Ak−1(z) f(k−1)+ · · · + A1(z) f0+ A0(z) f = 0, k ≥ 2 when most coefficients Aj(z) (j = 0, ..., k − 1) have the same ρϕ-order with each other. By using the concept of τϕ-type, we obtain some results which indicate growth estimate of every non-trivial entire solution of the above equations by the growth estimate of the coefficient A0(z) . We im- prove and generalize some recent results due to Chyzhykov-Semochko and the author.

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