An entire function and its derivatives sharing a polynomial |
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| Authors: | Xiao-Min Li Hong-Xun Yi |
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| Institution: | a Department of Mathematics, Ocean University of China, Qingdao, Shandong 266071, People's Republic of China
b Department of Mathematics, Shandong University, Jinan, Shandong 250100, People's Republic of China |
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| Abstract: | In this paper, we study the growth of solutions of a first-order linear differential equation and that of a second-order linear differential equation. From this we obtain some uniqueness theorems of a nonconstant entire function and its first derivative having the same fixed points with the same multiplicities. The results in this paper also improve some known results. Some examples show that the results in this paper are best possible. |
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| Keywords: | Entire function Order of growth Shared value Uniqueness |
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