<abstract xmlns="http://www.w3.org/1999/xhtml"><p> The aim of this work is to study asymptotic properties of the third-order quasi-linear delay differential equation <disp-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/v10127-011-0011-7#0007_graphic1.png"></inline-graphic></disp-formula>, (E) where <disp-formula><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="../graphic/v10127-011-0011-7#0007_graphic2.png"></inline-graphic></disp-formula> and τ(t) ≤ t. We establish a new condition which guarantees that every solution of (E) is either oscillatory or converges to zero. These results improve some known results in the literature. An example is given to illustrate the main results.</p></abstract>

The aim of this work is to study asymptotic properties of the third-order quasi-linear delay differential equation , (E) where  and τ(t) ≤ t. We establish a new condition which guarantees that every solution of (E) is either oscillatory or converges to zero. These results improve some known results in the literature. An example is given to illustrate the main results.

On the oscillation of third-order quasi-linear delay differential equations

School of Control Science and Engineering Shandong University, Jinan, Shandong 250061 P. R. China

Department of Mathematics Faculty of Electrical Engineering and Informatics Technical University of Koˇsice Letn´a 9 SK–042-00 Koˇsice SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"On the oscillation of third-order quasi-linear delay differential equations"}

The aim of this work is to study asymptotic properties of the third-order quasi-linear delay differential equation , (E) where  and τ(t) ≤ t. We establish a...

On the oscillation of third-order quasi-linear delay differential equations

Published Online: Nov 13, 2012

Page range: 117 - 123

DOI: https://doi.org/10.2478/v10127-011-0011-7

Keywords
third-order, delay differential equation, oscillation and asymptotic behavior

This content is open access.

On the oscillation of third-order quasi-linear delay differential equations

Published Online: Nov 13, 2012

Page range: 117 - 123

DOI: https://doi.org/10.2478/v10127-011-0011-7

Keywordsthird-order, delay differential equation, oscillation and asymptotic behavior

This content is open access.

Keywords
third-order, delay differential equation, oscillation and asymptotic behavior