On [p, q]-order of growth of solutions of linear differential equations in the unit disc
The $ [p, q] $-order of growth of solutions of the following linear differential equations $ (**) $ is investigated, $ f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f^{'}+A_{0}(z)f = 0, (**) $ where $ A_{i}(z) $ are analytic functions in the unit disc, $ i = 0, 1, ..., k-1 $. Some estimat...
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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.2021743?viewType=HTML |
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doaj-f2b120333a2a40c19ddb3d1c246f81312021-09-26T02:51:34ZengAIMS PressAIMS Mathematics2473-69882021-09-01611128781289310.3934/math.2021743On [p, q]-order of growth of solutions of linear differential equations in the unit discHongyan Qin0Jianren Long1Mingjin Li2School of Mathematical Science, Guizhou Normal University, Guiyang, 550025, ChinaSchool of Mathematical Science, Guizhou Normal University, Guiyang, 550025, ChinaSchool of Mathematical Science, Guizhou Normal University, Guiyang, 550025, ChinaThe $ [p, q] $-order of growth of solutions of the following linear differential equations $ (**) $ is investigated, $ f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f^{'}+A_{0}(z)f = 0, (**) $ where $ A_{i}(z) $ are analytic functions in the unit disc, $ i = 0, 1, ..., k-1 $. Some estimations of $ [p, q] $-order of growth of solutions of the equation $ (\ast*) $ are obtained when $ A_{j}(z) $ dominate the others coefficients near a point on the boundary of the unit disc, which is generalization of previous results from S. Hamouda.https://www.aimspress.com/article/doi/10.3934/math.2021743?viewType=HTMLlinear differential equationsunit disc[pq]-orderbounded point |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Hongyan Qin Jianren Long Mingjin Li |
| spellingShingle |
Hongyan Qin Jianren Long Mingjin Li On [p, q]-order of growth of solutions of linear differential equations in the unit disc AIMS Mathematics linear differential equations unit disc [p q]-order bounded point |
| author_facet |
Hongyan Qin Jianren Long Mingjin Li |
| author_sort |
Hongyan Qin |
| title |
On [p, q]-order of growth of solutions of linear differential equations in the unit disc |
| title_short |
On [p, q]-order of growth of solutions of linear differential equations in the unit disc |
| title_full |
On [p, q]-order of growth of solutions of linear differential equations in the unit disc |
| title_fullStr |
On [p, q]-order of growth of solutions of linear differential equations in the unit disc |
| title_full_unstemmed |
On [p, q]-order of growth of solutions of linear differential equations in the unit disc |
| title_sort |
on [p, q]-order of growth of solutions of linear differential equations in the unit disc |
| publisher |
AIMS Press |
| series |
AIMS Mathematics |
| issn |
2473-6988 |
| publishDate |
2021-09-01 |
| description |
The $ [p, q] $-order of growth of solutions of the following linear differential equations $ (**) $ is investigated,
$ f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f^{'}+A_{0}(z)f = 0, (**) $
where $ A_{i}(z) $ are analytic functions in the unit disc, $ i = 0, 1, ..., k-1 $. Some estimations of $ [p, q] $-order of growth of solutions of the equation $ (\ast*) $ are obtained when $ A_{j}(z) $ dominate the others coefficients near a point on the boundary of the unit disc, which is generalization of previous results from S. Hamouda. |
| topic |
linear differential equations unit disc [p q]-order bounded point |
| url |
https://www.aimspress.com/article/doi/10.3934/math.2021743?viewType=HTML |
| work_keys_str_mv |
AT hongyanqin onpqorderofgrowthofsolutionsoflineardifferentialequationsintheunitdisc AT jianrenlong onpqorderofgrowthofsolutionsoflineardifferentialequationsintheunitdisc AT mingjinli onpqorderofgrowthofsolutionsoflineardifferentialequationsintheunitdisc |
| _version_ |
1716868584053932032 |