两类非线性微分—差分方程的整函数解

Entire solutions of two types of nonlinear differential-difference equations

利用Nevanlinna值分布理论,研究了两类非线性微分-差分方程f^(n)+ωf^(n-1)f′+b(f′)^(n)+qe^(Q)f(z+c)=uev和f^(n)+ω_(1)f^(n-1)f′+ω_(2)(f′)^(n)+qe^(Q)f(z+c)=p_(1)e^(λ)_(1)^(z)+p_(2)e^(λ)_(2)^(z)的有限级整函数解的存在性,得到了两个结果,并举例证明文中所得结果是精确的。

Using Nevanlinna′s value distribution theory, this paper investigates the existence of entire solutions with finite order of two types of nonlinear differential-difference equations of the forms f^(n)+ωf^(n-1)f ′+b(f ′)^(n)+qe^(Q)f(z+c)=uevand f^(n)+ω_(1)f^(n-1)f ′+ω_(2)(f ′)^(n)+qe^(Q)f(z+c)=p_(1)e^(λ)_(1)^(z)+p_(2)e^(λ)_(2)^(z), and obtains two results. Examples are provided to show that the results obtained in this paper, in a sense, are best possible.