IJPAM: Volume 51, No. 4 (2009)

OSCILLATIONS FOR SECOND ORDER NEUTRAL
NONLINEAR DIFFERENTIAL EQUATIONS

Quan-Wen Lin$^1$, Rong-Kun Zhuang$^2$
$^1$Department of Mathematics
Maoming University
Maoming, 525000, P.R. CHINA
e-mail: linquanwen@126.com
$^2$Department of Mathematics
Huizhou University
Huizhou, Guangdong, 516015, P.R. CHINA
e-mail: rkzhuang@163.com


Abstract.Some new oscillation criteria are obtained for the second order neutral nonlinear differential equation of the form

\begin{displaymath} {[ r(t)[y(t)+p(t)y(\sigma (t))]^{\prime}]^{ \prime}+\sum_{i=1}^nq_i(t)f_i(y(\tau _i(t)))=0,\quad t\geq t_0\,.} \end{displaymath}

Our results improve some known results and show that the oscillation of some second order linear ordinary differential equations implies the oscillation of the nonlinear second order neutral delay differential equation.

Received: July 24, 2008

AMS Subject Classification: 34C10, 34K15

Key Words and Phrases: oscillation, nonlinear differential equation, neutral type, Rriccati transformation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 4