Address.
Q. Yang,
School of Mathematical Science, South China University of Technology,
Guangzhou, 510640 P. R. China
S.S. Cheng,
Department of Mathematics, Tsinghua University, Hsinchu, Taiwan 30043, R. O. China
E-mail.
qgyang@scut.edu.cn
sscheng@math.nthu.edu.tw
Abstract.
This paper is concerned with a class of even order nonlinear
differential equations of the form
\begin{multline*}
\frac{d}{dt}\Big( \Big|\left( x(t)+p(t)x(\tau (t))\right)
^{(n-1)}\Big| ^{\alpha -1}(x(t)+p(t)x(\tau (t)))^{(n-1)}\Big)\\
+F\big( t,x(g(t))\big) =0\,,
\end{multline*}
where $n$ is even and
$t\geq t_{0}$. By using the generalized Riccati transformation and
the averaging technique, new oscillation criteria are obtained which
are either extensions of or complementary to a number of existing
results. Our results are more general and sharper than some previous
results even for second order equations.
AMSclassification.
34A30, 34K11.
Keywords.
Neutral differential equation, oscillation criterion,
Riccati transform, averaging method.