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On transcendental directions of entire solutions of linear differential equations
oleh: Zheng Wang, Zhi Gang Huang
| Format: | Article |
|---|---|
| Diterbitkan: | AIMS Press 2022-01-01 |
Deskripsi
This paper is devoted to studying the transcendental directions of entire solutions of $ f^{(n)}+A_{n-1}f^{(n-1)}+...+A_0f = 0 $, where $ n(\geq 2) $ is an integer and $ A_i(z)(i = 0, 1, ..., n-1) $ are entire functions of finite lower order. With some additional conditions, the set of common transcendental directions of non-trivial solutions, their derivatives and their primitives must have a definite range of measure. Moreover, we obtain the lower bound of the measure of the set defined by the common transcendental directions of Jackson difference operator of non-trivial solutions.