Electron. J. Diff. Equ., Vol. 2011 (2011), No. 23, pp. 1-12.

Oscillation of solutions to odd-order nonlinear neutral functional differential equations

Tongxing Li, Ethiraju Thandapani

Abstract:
In this note, we establish some new comparison theorems and Philos-type criteria for oscillation of solutions to the odd-order nonlinear neutral functional differential equation
$$ [x(t)+p(t)x(\tau(t))]^{(n)}+q(t)x^\alpha(\sigma(t))=0, $$
where $0\leq p(t)\leq p_0<\infty$ and $\alpha\geq1$.

Submitted January 13, 2011. Published February 9, 2011.
Math Subject Classifications: 34K11, 34C10.
Key Words: Odd-order; neutral differential equation; oscillation; asymptotic behavior.

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Tongxing Li
School of Control Science and Engineering
Shandong University
Jinan, Shandong 250061, China
email: litongx2007@163.com
Ethiraju Thandapanii
Ramanujan Institute for Advanced Study in Mathematics
University of Madras, Chennai, India
email: ethandapani@yahoo.co.in

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