J. Korean Math. Soc. 2011; 48(3): 499-512
Printed May 1, 2011
https://doi.org/10.4134/JKMS.2011.48.3.499
Copyright © The Korean Mathematical Society.
Feng L\"{u} and Hongxun Yi
China University of Petroleum, Shandong University
The purpose of this paper is twofold. The first is to establish a uniqueness theorem for entire function sharing two polynomials with its $k$-th derivative, by using the theory of normal families. Meanwhile, the theorem generalizes some related results of Rubel and Yang and of Li and Yi. Several examples are provided to show the conditions are necessary. The second is to generalize the Br\"{u}ck conjecture with the idea of sharing polynomial.
Keywords: Vandermonde determinant, entire functions, Nevanlinna theory, uniqueness, normal family, differential equation
MSC numbers: 30D35, 30D45
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