Open AccessOn transcendental directions of entire solutions of linear differential equations
Author(s) -
Zheng Wang,
Zhi Gang Huang
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022018
Subject(s) - transcendental number , mathematics , transcendental equation , transcendental function , measure (data warehouse) , integer (computer science) , set (abstract data type) , entire function , order (exchange) , range (aeronautics) , operator (biology) , differential equation , discrete mathematics , pure mathematics , combinatorics , mathematical analysis , computer science , chemistry , biochemistry , materials science , finance , repressor , database , transcription factor , economics , composite material , gene , programming language
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.