Abstract
In this paper, we precise the hyper order of solutions for a class of higher-order linear differential equations and investigate the exponents of convergence of the fixed points of solutions and their first derivatives for the second-order case. These results generalize those of Nan Li and Lianzhong Yang and of Chen and Shon.
Highlights
I n this paper, we use standard notations from the value distribution theory of meromorphic functions
In this paper, we precise the hyper order of solutions for a class of higher order linear differential equations and investigate the exponents of convergence of the fixed points of solutions and their first derivatives for the second order case
These results generalize those of Nan Li and Lianzhong Yang and of Chen and Shon
Summary
I n this paper, we use standard notations from the value distribution theory of meromorphic functions (see [1–3]). 2021, 5(2), 1-16 where Pj(ez) (j = 0, · · · , k − 1) are polynomials in z, Yang and Li [11] generalized the result of Theorem 2 to the higher order and obtained the following results: Set ajmj (z) = ajmjdjmj zdjmj + ajmj(djmj −1)zdjmj −1 + · · · + ajmj1z + ajmj0, (5) where djmj ≥ 0 (j = 0, · · · , k − 1) are integers, ajmjdjmj , ..., ajmj0 are complex constants, ajmjdjmj = 0. [11] Under the assumption of Theorem 4, if zP0(ez) + P1(ez) ≡ 0, we have every solution f ≡ 0 of Equation (4) satisfies τ2( f ) = τ2( f ) = ρ2 ( f ) = 1 They investigated the exponents of convergence of the fixed points of solutions and their first derivatives for a second order Equation (1) and obtained the following theorem: Theorem 6.
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