Electron. J. Diff. Equ., Vol. 2010(2010), No. 73, pp. 1-9.

Oscillation criteria for forced second-order mixed type quasilinear delay differential equations

Sowdaiyan Murugadass, Ethiraju Thandapani, Sandra Pinelas

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.

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Sowdaiyan Murugadass
Ramanujan Institute for Advanced Study in Mathematics
University of Madras, Chennai - 600005, India
email: murugadasssm@gmail.com
Ethiraju Thandapani
Ramanujan Institute for Advanced Study in Mathematics
University of Madras, Chennai - 600005, India
email: ethandapani@yahoo.co.in
Sandra Pinelas
Departamento de Matemática
Universidade dos Açores, Portugal
email: sandra.pinelas@clix.pt

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