Electron. J. Diff. Equ., Vol. 2011 (2011), No. 143, pp. 1-9.

Oscillation results for even-order quasilinear neutral functional differential equations

Blanka Baculikova, Jozef Dzurina, Tongxing Li

Abstract:
In this article, we use the Riccati transformation technique and some inequalities, to establish oscillation theorems for all solutions to even-order quasilinear neutral differential equation
$$ \Big(\big[\big(x(t)+p(t)x(\tau(t))\big)^{(n-1)}\big]^\gamma\Big)' +q(t)x^\gamma\big(\sigma(t)\big)=0,\quad t\geq t_0. $$
Our main results are illustrated with examples.

Submitted April 28, 2011. Published November 1, 2011.
Math Subject Classifications: 34K11, 34C10.
Key Words: Oscillation; Neutral differential equation; even-order.

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  Blanka Baculíková
Department of Mathematics
Faculty of Electrical Engineering and Informatics
Technical University of Kosice
Letná 9, 042 00 Kosice, Slovakia
email: blanka.baculikova@tuke.sk
Jozef Dzurina
Department of Mathematics
Faculty of Electrical Engineering and Informatics
Technical University of Kosice
Letná 9, 042 00 Kosice, Slovakia
email: jozef.dzurina@tuke.sk
Tongxing Li
School of Control Science and Engineering
Shandong University
Jinan, Shandong 250061, China
email: litongx2007@163.com

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