Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 10, pp. 1-11.
Title: Oscillation criteria for second-order neutral differential
equations with distributed deviating arguments
Authors: Gaihua Gui (South China Normal Univ., China)
Zhiting Xu (South China Normal Univ., China)
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.