Oscillation criteria for a class of third order neutral distributed delay differential equations with damping

Volume 19, Issue 1, pp 19--28 http://dx.doi.org/10.22436/jmcs.019.01.03

Publication Date: March 02, 2019 Submission Date: January 20, 2019 Revision Date: February 04, 2019 Accteptance Date: February 11, 2019

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Authors

M. H. Wei - School of Mathematics and Statistics, Yulin University, Yulin 719000, China. M. L. Zhang - School of Mathematics and Statistics, Yulin University, Yulin 719000, China. X. L. Liu - School of Mathematics and Statistics, Yulin University, Yulin 719000, China. Y. H. Yu - Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China.

Abstract

In this paper, the oscillation criteria of a class of third order neutral distributed delay differential equations with damping are investigated. This work is the continuation of the study by Saker [S. H. Saker, Math. Slovaca, \({\bf 56}\) (2006), 433--450] and the extension of the work by Zhang [Q. X. Zhang, L. Gao, Y. H. Yu, Appl. Math. Lett., \({\bf 25}\) (2012), 1514--1519] on oscillation properties of nonlinear third order delay differential equation. By choosing the appropriate functions and using a generalized Riccati transformation, some new oscillation criteria are presented to insure that every solution of this equation oscillates or converges to zero. The presented results correct and improve the earlier ones in existing literature. Finally, several illustrative examples are included.

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Keywords

• Oscillation criteria
• third order
• distributed delay
• damping
• Riccati transformation

MSC

•  34C10
•  34K11

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