Electron. J. Diff. Equ., Vol. 2012 (2012), No. 29, pp. 1-9.

Oscillation of solutions to third-order half-linear neutral differential equations

Jozef Dzurina, Ethiraju Thandapani, Sivaraj Tamilvanan

Abstract:
In this article, we study the oscillation of solutions to the third-order neutral differential equations
$$ \Big(a(t)\big([x(t)\pm p(t)x(\delta(t))]''\big)^\alpha\Big)' + q(t)x^\alpha(\tau(t)) = 0. $$
Sufficient conditions are established so that every solution is either oscillatory or converges to zero. In particular, we extend the results obtain in [1] for $a(t)$ non-decreasing, to the non-increasing case.

Submitted November 12, 2011. Published February 21, 2012.
Math Subject Classifications: 34K11, 34C10.
Key Words: Third-order neutral differential equation; Riccati transformation; oscillation of solutions.

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Jozef Dzurina
Department of Mathematics
Faculty of Electrical Engineering and Informatics
Technical University of Kosice
Letna 9, 042 00 Kosice, Slovakia
email: jozef.dzurina@tuke.sk
Ethiraju Thandapani
Ramanujan Institute for Advanced Study in Mathematics
University of Madras, Chennai, 600 005, India
email: ethandapani@yahoo.co.in
Sivaraj Tamilvanan
Ramanujan Institute for Advanced Study in Mathematics
University of Madras, Chennai, 600 005, India
email: saitamilvanan@yahoo.in

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