Oscillation of arbitrary-order derivatives of solutions to the higher order non-homogeneous linear differential equations taking small functions in the unit disc
In this article, we study the relationship between solutions and their arbitrary-order derivatives of the higher order non-homogeneous linear differential equation $ \begin{equation*} f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f'+A_{0}(z)f = F(z) \end{equation*} $ in the unit disc $ \bigt...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021798?viewType=HTML |
| _version_ | 1818977286039273472 |
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| author | Pan Gong Hong Yan Xu |
| author_facet | Pan Gong Hong Yan Xu |
| author_sort | Pan Gong |
| collection | DOAJ |
| description | In this article, we study the relationship between solutions and their arbitrary-order derivatives of the higher order non-homogeneous linear differential equation
$ \begin{equation*} f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f'+A_{0}(z)f = F(z) \end{equation*} $
in the unit disc $ \bigtriangleup $ with analytic or meromorphic coefficients of finite $ [p, q] $-order. We obtain some oscillation theorems for $ f^{(j)}(z)-\varphi(z) $, where $ f $ is a solution and $ \varphi(z) $ is a small function. |
| first_indexed | 2024-12-20T16:25:19Z |
| format | Article |
| id | doaj.art-b8076a04005d4be8bc1a45807769e33d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-20T16:25:19Z |
| publishDate | 2021-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-b8076a04005d4be8bc1a45807769e33d2022-12-21T19:33:27ZengAIMS PressAIMS Mathematics2473-69882021-09-01612137461375710.3934/math.2021798Oscillation of arbitrary-order derivatives of solutions to the higher order non-homogeneous linear differential equations taking small functions in the unit discPan Gong0Hong Yan Xu1School of Mathematics and Computer Science, Shangrao Normal University, Shangrao Jiangxi 334001, ChinaSchool of Mathematics and Computer Science, Shangrao Normal University, Shangrao Jiangxi 334001, ChinaIn this article, we study the relationship between solutions and their arbitrary-order derivatives of the higher order non-homogeneous linear differential equation $ \begin{equation*} f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f'+A_{0}(z)f = F(z) \end{equation*} $ in the unit disc $ \bigtriangleup $ with analytic or meromorphic coefficients of finite $ [p, q] $-order. We obtain some oscillation theorems for $ f^{(j)}(z)-\varphi(z) $, where $ f $ is a solution and $ \varphi(z) $ is a small function.https://www.aimspress.com/article/doi/10.3934/math.2021798?viewType=HTMLunit discnon-homogeneous linear differential equationarbitrary-order derivativesmall function |
| spellingShingle | Pan Gong Hong Yan Xu Oscillation of arbitrary-order derivatives of solutions to the higher order non-homogeneous linear differential equations taking small functions in the unit disc AIMS Mathematics unit disc non-homogeneous linear differential equation arbitrary-order derivative small function |
| title | Oscillation of arbitrary-order derivatives of solutions to the higher order non-homogeneous linear differential equations taking small functions in the unit disc |
| title_full | Oscillation of arbitrary-order derivatives of solutions to the higher order non-homogeneous linear differential equations taking small functions in the unit disc |
| title_fullStr | Oscillation of arbitrary-order derivatives of solutions to the higher order non-homogeneous linear differential equations taking small functions in the unit disc |
| title_full_unstemmed | Oscillation of arbitrary-order derivatives of solutions to the higher order non-homogeneous linear differential equations taking small functions in the unit disc |
| title_short | Oscillation of arbitrary-order derivatives of solutions to the higher order non-homogeneous linear differential equations taking small functions in the unit disc |
| title_sort | oscillation of arbitrary order derivatives of solutions to the higher order non homogeneous linear differential equations taking small functions in the unit disc |
| topic | unit disc non-homogeneous linear differential equation arbitrary-order derivative small function |
| url | https://www.aimspress.com/article/doi/10.3934/math.2021798?viewType=HTML |
| work_keys_str_mv | AT pangong oscillationofarbitraryorderderivativesofsolutionstothehigherordernonhomogeneouslineardifferentialequationstakingsmallfunctionsintheunitdisc AT hongyanxu oscillationofarbitraryorderderivativesofsolutionstothehigherordernonhomogeneouslineardifferentialequationstakingsmallfunctionsintheunitdisc |