Asymptotic behavior criteria for solutions of nonlinear third order neutral differential equations

Volume 17, Issue 2, pp 325-331 http://dx.doi.org/10.22436/jmcs.017.02.15

Publication Date: June 15, 2017 Submission Date: October 01, 2016

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Authors

Hussain Ali Mohamad - Department of mathematics, College of science for women, University of Baghdad, IRAQ. Sattar Naser Ketab - Department of Mathematics, College of education, University of Kufa, IRAQ.

Abstract

In this paper the asymptotic behavior for all nonoscillatory solutions of third order nonlinear neutral differential equations have been investigated, where some necessary and sufficient conditions are obtained to guarantee the convergence of these solutions to zero or tends to infinity as \(t\rightarrow\infty\). We introduced Lemma 2.1 and Lemma 2.2 which are a generalization of Lemma 1.5.2 [I. Győri, G. Ladas, Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, (1991)]. Some examples are given to illustrate our main results.

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Keywords

• Oscillation
• asymptotic behavior
• neutral differential equations.

MSC

•  34K11

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