机构地区: 江苏第二师范学院数学与信息技术学院,南京210013
出 处: 《中国科学:数学》 2017年第8期919-932,共14页
摘 要: 本文主要考虑下列形式的非线性微分方程的超越亚纯解:f^nf~′+Q_d(z,f)=p_1(z)e^(α_1(z))+p_2(z)e^(α_2(z)),其中n≥3是一个整数,Q_d(z,f)是一个关于f的次数d≤n-2且以有理函数为系数的微分多项式,p_1和p_2是非零的有理函数,α_1和α_2是非常数的多项式.进一步地,本文给出了上述方程存在亚纯解时α′_1/α′_2所满足的条件.这些结果推广并改进了一些已知的结果. In this paper, we consider the transcendental meromorphic solutions of nonlinear differential equation of the form f^nf^′+ Qd(z, f) = p1(z)e^α1(z))+ p2(z)e^(α2(z)),where n≥3 is an integer, Qd(z, f) is a differential polynomial in f of degree d≤n-2 with rational functions as its coefficients, p1, p2 are nonzero rational functions and α1, α2 are nonconstant polynomials. More precisely,we show that the conditions concerningα′1α′2will ensure the existence of the possible meromorphic solutions of the above equation. These results extend and improve some known results obtained most recently.