**Zhiting Xu, Peixuan Weng**

## Oscillation Theorems for Certain Even
Order Delay Differential Equations Involving General Means

**Abstract:**

By using the general means, we establish some oscillation theorems for the even
order delay differential equation

$$ (r(t)|x^{(n-1)}(t)|^{\alpha-1}x^{(n-1)}(t))^{\prime}+F(t, x[g(t)])=0, $$

where $\alpha >0$ is a constant, $r \in C^1([t_0, \infty), \mathbb{R}_+)$, $F
\in C([t_0, \infty)\times \mathbb{R}, \mathbb{R})$, and $g \in C([t_0, \infty),
\mathbb{R})$. The results obtained extend and improve some results known in the
literature.

**Keywords:**

Oscillation, delay differential equation, even order, general means.

**MSC 2000:** 34K11, 34C10