Abstract
The growth of solutions of complex linear differential equation \(f^{\prime \prime }+Af^{\prime }+Bf=0\) is studied, where A(z) and B(z) are entire functions. With some conditions on A(z) and B(z), we prove that every non-trivial solution f of the equation is of infinite order. Moreover, we obtain the lower bound of measure of angular domain, in which the radial order of f is infinite. Some examples are given to illustrate the results.
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Acknowledgements
The authors would like to thank the referee for valuable comments to improve the present article. The third author is supported by the National Natural Science Foundation of China (Grant Nos. 11861023, 11501142) and the Foundation of Science and Technology project of Guizhou Province of China (Grant No. [2018]5769-05). The fourth author is supported by National Natural Science Foundation of China (Grant Nos. 11571049, 11101048).
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Communicated by Pham Huu Anh Ngoc.
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Qiao, J., Zhang, Q., Long, J. et al. A Note on the Growth of Solutions of Second-Order Complex Linear Differential Equations. Bull. Malays. Math. Sci. Soc. 43, 2137–2150 (2020). https://doi.org/10.1007/s40840-019-00796-8
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DOI: https://doi.org/10.1007/s40840-019-00796-8