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.