IJPAM: Volume 48, No. 2 (2008)

OSCILLATION CRITERIA FOR SECOND ORDER
DIFFERENTIAL EQUATIONS WITH DISTRIBUTED
DEVIATING ARGUMENTS AND A DAMPING TERM

Hui-Zeng Qin$^1$, Youmin Lu$^2$
$^1$Department of Mathematics and Information Technology
Shandong University of Technology
Zibo, Shandong, P.R. CHINA
e-mail: qinhz_000@163.com
$^2$Department of Mathematics and Computer Science
Bloomsburg University,
Bloomsburg, PA 17915, USA
e-mail: ylu@bloomu.edu


Abstract.We study the second order differential equation $[r(x)\psi (y(x))(y(x)+c(x)y(d(x)))^{\prime }]^{\prime }+\int_{\alpha }^{\beta }a(x,\theta )f(y(b(x,\theta )))d\theta =0$ and establish some criteria for the solutions of this equation to be oscillatory that extend the existing results.

Received: August 20, 2008

AMS Subject Classification: 34C10, 34K11, 34K40

Key Words and Phrases: oscillatory, second order non-linear differential equations, distributed arguments, damping term

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 48
Issue: 2