Abstract
In this paper, we deal with the relationship between the small function and the derivative of solutions of higher order linear differential equations f ( k ) + A k − 1 f ( k − 1 ) +⋯+ A 0 f=0(k≥2), where A j (z) (j=0,1,…,k−1) are entire functions or meromorphic functions. The theorems of this paper improve the previous results given by Chen, Belaïdi, Liu.MSC:34M10, 30D35.
Highlights
Introduction and main resultsComplex oscillation theory of solutions of linear differential equations in the complex plane C was started by Bank and Laine [, ]
(ii) we show that Uji (j =, . . . , k – ) satisfy ( ) when i =
Suppose that max{σ (Aj) : j =, . . . , k – } < σ (A ) < ∞. (i) First, we prove that λ (f – φ) = σ (f )
Summary
Introduction and main resultsComplex oscillation theory of solutions of linear differential equations in the complex plane C was started by Bank and Laine [ , ]. Theorem D (see [ ]) Suppose that k ≥ and A(z) is a transcendental meromorphic function satisfying δ(∞, A)
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