Infinite growth of solutions of second order complex differential equations with meromorphic coefficients

Zheng Wang; Zhi Gang Huang; Zheng Wang; Zhi Gang Huang

doi:10.3934/math.2022379

AIMS Mathematics

2022, Volume 7, Issue 4: 6807-6819. doi: 10.3934/math.2022379

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Research article

Infinite growth of solutions of second order complex differential equations with meromorphic coefficients

Zheng Wang ,
Zhi Gang Huang ^,

School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, China

Received: 25 December 2021 Revised: 18 January 2022 Accepted: 19 January 2022 Published: 26 January 2022
MSC : 30D35, 34M10, 37F10

This paper is devoted to studying the growth of solutions of $ f''+A(z)f'+B(z)f = 0 $, where $ A(z) $ and $ B(z) $ are meromorphic functions. With some additional conditions, we show that every non-trivial solution $ f $ of the above equation has infinite order. In addition, we also obtain the lower bound of measure of the angular domain, in which the radial order of $ f $ is infinite.
- meromorphic function,
- infinite growth,
- complex differential equation,
- radial order
Citation: Zheng Wang, Zhi Gang Huang. Infinite growth of solutions of second order complex differential equations with meromorphic coefficients[J]. AIMS Mathematics, 2022, 7(4): 6807-6819. doi: 10.3934/math.2022379

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Abstract

This paper is devoted to studying the growth of solutions of $ f''+A(z)f'+B(z)f = 0 $, where $ A(z) $ and $ B(z) $ are meromorphic functions. With some additional conditions, we show that every non-trivial solution $ f $ of the above equation has infinite order. In addition, we also obtain the lower bound of measure of the angular domain, in which the radial order of $ f $ is infinite.

References

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