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