Electron. J. Diff. Eqns., Vol. 2007(2007), No. 10, pp. 1-11.

Oscillation criteria for second-order neutral differential equations with distributed deviating arguments

Gaihua Gui, Zhiting Xu

Abstract:
Using a class of test functions $\Phi(t,s,T)$ defined by Sun [13] and a generalized Riccati technique, we establish some new oscillation criteria for the second-order neutral differential equation with distributed deviating argument
$$ (r(t)\psi(x(t))Z'(t))'+\int^b_a q(t,\xi)f[x(g(t,\xi))]d\sigma(\xi)=0,\quad t\geq t_0, $$
where $Z(t)=x(t)+p(t)x(t-\tau)$. The obtained results are different from most known ones and can be applied to many cases which are not covered by existing results.

Submitted July 28, 2006. Published January 2, 2007.
Math Subject Classifications: 34K11, 34C10, 34K40.
Key Words: Oscillation; neutral differential equation; second order; distributed deviating argument; Riccati technique.

Show me the PDF file (242K), TEX file, and other files for this article.

Gaihua Gui
School of Mathematical Sciences
South China Normal University
Guangzhou, 510631, China
email: 1981hgg@163.com
Zhiting Xu
School of Mathematical Sciences
South China Normal University
Guangzhou, 510631, China
email: xztxhyyj@pub.guangzhou.gd.cn

Return to the EJDE web page