Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 58, pp. 1-9.

Title: Interval oscillation of second-order Emden-Fowler neutral delay
       differential equations

Authors: Mu Chen    (South China Normal Univ., China)
         Zhiting Xu (South China Normal Univ., China)

Abstract:
 Employing  Riccati techniques and the integral averaging method,
 we establish interval oscillation criteria  for the second-order
 Emden-Fowler neutral delay differential equation
 $$
 [|x'(t)|^{\gamma-1}x'(t)]'+q_1(t)|y(t-\sigma)|^{\alpha-1}y(t-\sigma)
 +q_2(t)|y(t-\sigma)|^{\beta-1} y(t-\sigma)=0,
 $$
 where $t\geq t_0$ and $x(t)=y(t)+p(t)y(t-\tau)$.  The criteria
 obtained here are different from most known criteria in the sense
 that they are based on information only on a sequence of subintervals
 of $[t_0,\infty)$, rather than on the whole half-line. In particular,
 two interesting examples that illustrate the importance of our results
 are included.
  
Submitted January 5, 2007. Published April 22, 2007.
Math Subject Classifications: 34K40, 34K11, 34C10.
Key Words: Interval oscillation; neutral delay differential equation;
           Emden-Fowler; Riccati technique; integral averaging method.