Georgian Mathematical Journal 13 (2006), No. 2, 383--394
Copyright Heldermann Verlag 2006
Oscillation Theorems for Certain Even Order Delay Differential Equations Involving General Means
Zhiting Xu
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China
xztxhyyj@pub.guangzhou.gd.cn
Peixuan Weng
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, P. R. China
[Abstract-pdf]
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: 34K11, 34C10
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