Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses
American Journal of Applied Mathematics
Volume 5, Issue 4, August 2017, Pages: 119-123
Received: Oct. 20, 2016; Accepted: Nov. 14, 2016; Published: Aug. 24, 2017
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Authors
Ubon Akpan Abasiekwere, Department of Mathematics and Statistics, Faculty of Science, University of Uyo, Uyo, Nigeria
Edwin Frank Nsien, Department of Mathematics and Statistics, Faculty of Science, University of Uyo, Uyo, Nigeria
Imoh Udo Moffat, Department of Mathematics and Statistics, Faculty of Science, University of Uyo, Uyo, Nigeria
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Abstract
In this paper, we study a certain type of second order linear neutral differential equation with constant impulsive jumps. This type of equation is known always to possess an unbounded non-oscillatory solution. The method and technique of impulse imposition used here is due to studies by Bainov and Simeonov [1]. By assuming, amongst other conditions, that the constant coefficient of the equation in question lies between zero and one and the delay function is non-decreasing, it is shown that all bounded solutions of the said neutral impulsive equation are oscillatory.
Keywords
Bounded, Oscillations, Second-order, Neutral, Delay, Impulsive, Differential Equation
To cite this article
Ubon Akpan Abasiekwere, Edwin Frank Nsien, Imoh Udo Moffat, Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses, American Journal of Applied Mathematics. Vol. 5, No. 4, 2017, pp. 119-123. doi: 10.11648/j.ajam.20170504.14
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Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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