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.
Citation: Hongyan Qin, Jianren Long, Mingjin Li. On [p, q]-order of growth of solutions of linear differential equations in the unit disc[J]. AIMS Mathematics, 2021, 6(11): 12878-12893. doi: 10.3934/math.2021743
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.
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Hongyan Qin, Jianren Long, Mingjin Li. On [p, q]-order of growth of solutions of linear differential equations in the unit disc[J]. AIMS Mathematics, 2021, 6(11): 12878-12893. doi: 10.3934/math.2021743
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