Shimei Zhang’s research while affiliated with Guizhou Normal University and other places

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Publications (2)


Second-Order Linear Differential Equations with Solutions in Analytic Function Spaces
  • Article
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February 2019

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155 Reads

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4 Citations

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Shimei Zhang

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This research is concerned with second-order linear differential equation f ′ ′ + A ( z ) f = 0 , where A ( z ) is an analytic function in the unit disc. On the one hand, some sufficient conditions for the solutions to be in α -Bloch (little α -Bloch) space are found by using exponential type weighted Bergman reproducing kernel formula. On the other hand, we find also some sufficient conditions for the solutions to be in analytic Morrey (little analytic Morrey) space by using the representation formula.

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On a question of Gundersen concerning the growth of solutions of linear differential equations

February 2018

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232 Reads

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21 Citations

Annales Academiae Scientiarum Fennicae Mathematica

We prove that every nontrivial solution of f" + A(z)f' + Q(z)f = 0 is of infinite order, where A(z) is an entire function satisfying λ(A) < ρ(A) < ∞ and some restrictions, and Q(z) is a non-constant polynomial. This result gives partial solutions to a question posed by Gundersen. Related results are also given.

Citations (2)


... where A i (z) are analytic in the unit disc ∆ = {z : |z| < 1}, i = 0, 1, ..., k − 1, k ≥ 2. For the properties of solutions of Eq (1.1), including growth, zero distribution and function space properties, many results have been obtained, for example [9,10,14,16,20,22,23,25] and therein references. In addition, the differential equations have wide applications in various science discipline, for example engineering, predator-prey equations, population growth and decay, Newton's law of cooling and so on, see [1,5,24,28,29] and therein references. ...

Reference:

On [p, q]-order of growth of solutions of linear differential equations in the unit disc
Second-Order Linear Differential Equations with Solutions in Analytic Function Spaces

... The general problem of Ozawa has been proposed by Heittokangas, and given by Gundersen, see [10,Section 5]. More and more papers focus on the existence of finite order solutions of second linear differential equations (1.3) with entire coefficients, even precise form of finite order solutions, see [14,15,17,24,36,39]. ...

On a question of Gundersen concerning the growth of solutions of linear differential equations

Annales Academiae Scientiarum Fennicae Mathematica