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Entire Solutions of Two Certain Types of Non-linear Differential-Difference Equations
Computational Methods and Function Theory ( IF 0.6 ) Pub Date : 2020-08-08 , DOI: 10.1007/s40315-020-00343-8 Wei Chen , Peichu Hu , Qiong Wang
中文翻译:
两种特定类型的非线性微分方程的整体解
更新日期:2020-08-08
Computational Methods and Function Theory ( IF 0.6 ) Pub Date : 2020-08-08 , DOI: 10.1007/s40315-020-00343-8 Wei Chen , Peichu Hu , Qiong Wang
In this paper, we describe entire solutions for two certain types of non-linear differential-difference equations of the form
$$\begin{aligned} f^n(z)+\omega f^{n-1}(z)f'(z)+q(z)e^{Q(z)}f(z+c)=u(z)e^{v(z)}, \end{aligned}$$and
$$\begin{aligned} f^n(z)+\omega f^{n-1}(z)f'(z)+q(z)e^{Q(z)}f(z+c)=p_1e^{\lambda z}+p_2e^{-\lambda z}, \end{aligned}$$where q, Q, u, v are non-constant polynomials, \(c,\lambda ,p_1,p_2\) are non-zero constants, and \(\omega \) is a constant. Our results improve and generalize some previous results.
中文翻译:
两种特定类型的非线性微分方程的整体解
在本文中,我们描述了两种形式的非线性微分方程的整体解
$$ \ begin {aligned} f ^ n(z)+ \ omega f ^ {n-1}(z)f'(z)+ q(z)e ^ {Q(z)} f(z + c) = u(z)e ^ {v(z)},\ end {aligned} $$和
$$ \ begin {aligned} f ^ n(z)+ \ omega f ^ {n-1}(z)f'(z)+ q(z)e ^ {Q(z)} f(z + c) = p_1e ^ {\ lambda z} + p_2e ^ {-\ lambda z},\ end {aligned} $$其中q, Q, u, v是非常数多项式,\(c,\ lambda,p_1,p_2 \)是非零常数,而\(\ omega \)是常数。我们的结果改进并概括了以前的一些结果。