Taiwanese Journal of Mathematics

OSCILLATION OF THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Ravi Agarwal, Martin Bohner, Tongxing Li, and Chenghui Zhang

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Abstract

In this paper, we study the oscillatory behavior of a class of third-order nonlinear delay differential equations $$ (a(t) (b(t) y'(t))')' + q(t) y^\gamma(\tau(t)) = 0. $$ Some new oscillation criteria are presented by transforming this equation to the first-order delayed and advanced differential equations. Employing suitable comparison theorems we establish new results on oscillation of the studied equation. Assumptions in our theorems are less restrictive, these criteria improve those in the recent paper [Appl. Math. Comput., 202 (2008), 102-112] and related contributions to the subject. Examples are provided to illustrate new results.

Article information

Source
Taiwanese J. Math., Volume 17, Number 2 (2013), 545-558.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499705953

Digital Object Identifier
doi:10.11650/tjm.17.2013.2095

Mathematical Reviews number (MathSciNet)
MR3044522

Zentralblatt MATH identifier
1286.34099

Subjects
Primary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory 34K11: Oscillation theory

Keywords
third-order nonlinear equation delay differential equation oscillatory solution

Citation

Agarwal, Ravi; Bohner, Martin; Li, Tongxing; Zhang, Chenghui. OSCILLATION OF THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS. Taiwanese J. Math. 17 (2013), no. 2, 545--558. doi:10.11650/tjm.17.2013.2095. https://projecteuclid.org/euclid.twjm/1499705953


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