All admissible meromorphic solutions of certain type of second degree second order algebraic ODEs

作者：Zhang, Yueyang^*; Gao, Zongsheng; Zhang, Jilong

来源：Journal of Mathematical Analysis and Applications, 2017, 452(2): 1182-1193.

DOI：10.1016/j.jmaa.2017.03.054

• Admissible
• Meromorphic solutions
• Differential equations
• Hayman's conjecture

Following the same idea of Halburd and Wang [9] to construct small functions of w and w' by using the first one or two terms in the local series expansion for w at zeros, we solve all the admissible meromorphic solutions of the second order algebraic differential equation w '' w - w'(2) + aww' + bw(2) + bw(2) = alpha w + beta w' + gamma, where a, b are constants and alpha, beta,gamma are small meromorphic functions of w in the sense of Nevanlinna theory. These solutions can have infinite order as Hayman [11] has pointed out but still holds for his conjecture that T(r,w) <= c(1)e(c2rc), 0 <= r < +infinity when alpha,beta,gamma are rational functions, where c(1), c(2) and c are some positive constants.

• 出版日期2017-8-15
• 单位北京航空航天大学