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.

Show me the PDF file (233 KB), TEX file, and other files for this article.

  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

Return to the EJDE web page