Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 73, pp. 1-9.
Title: Oscillation criteria for forced second-order mixed
type quasilinear delay differential equations
Authors: Sowdaiyan Murugadass (Univ. of Madras, Chennai, India)
Ethiraju Thandapani (Univ. of Madras, Chennai, India)
Sandra Pinelas (Univ. dos Acores, Portugal)
Abstract:
This article presents new oscillation criteria
for the second-order delay differential equation
$$
(p(t) (x'(t))^{\alpha})' + q(t) x^{\alpha}(t - \tau) +
\sum_{i = 1}^{n} q_{i}(t) x^{\alpha_{i}}(t - \tau) = e(t)
$$
where $\tau \geq 0$, $p(t) \in C^1[0, \infty)$,
$q(t),q_{i}(t), e(t) \in C[0, \infty)$, $p(t) > 0$,
$\alpha_1 >\dots > \alpha_{m} > \alpha > \alpha_{m+1}
> \dots > \alpha_{n} > 0\ (n > m\geq 1)$,
$\alpha_1, \dots , \alpha_{n}$
and $\alpha$ are ratio of odd positive integers. Without assuming
that $q(t), q_{i}(t)$ and $e(t)$ are nonnegative, the results in [6,8]
have been extended and a mistake in the proof of the
results in [3] is corrected.
Submitted January 10, 2010. Published May 19, 2010.
Math Subject Classifications: 34K11, 34C55.
Key Words: Interval oscillation; quasilinear delay differential equation;
second order.