Borel directions of solutions of a second order linear complex differential equation

WEI Wen-long; HUANG Zhi-gang

doi:10.3969/j.issn.1000-5641.2019.02.005

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WEI Wen-long, HUANG Zhi-gang. Borel directions of solutions of a second order linear complex differential equation[J]. Journal of East China Normal University (Natural Sciences), 2019, (2): 49-55. doi: 10.3969/j.issn.1000-5641.2019.02.005

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WEI Wen-long, HUANG Zhi-gang. Borel directions of solutions of a second order linear complex differential equation[J]. Journal of East China Normal University (Natural Sciences), 2019, (2): 49-55. doi: 10.3969/j.issn.1000-5641.2019.02.005

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Borel directions of solutions of a second order linear complex differential equation

doi: 10.3969/j.issn.1000-5641.2019.02.005

WEI Wen-long,
HUANG Zhi-gang^,

School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou Jiangsu 215000, China

Received Date: 2018-01-13
Publish Date: 2019-03-25

Abstract

Abstract

In this paper, we consider the Borel directions of solutions of the differential equation f" + A(z)f' +B(z)f=0. By using Nevanlinna's value distribution theory and assuming that A(z) is extremal for Yang's inequality, we provide conditions for B(z) that guarantee that every non-trivial solution f of the equation is of infinite order; we also calculate the number of Borel directions of these solutions.
- infinite order,
- Borel directions,
- Yang's inequality,
- Fabry gap series,
- Baker wandering domain

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References(12)

References

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