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：

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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。