Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses

Ubon Akpan Abasiekwere; Edwin Frank Nsien; Imoh Udo Moffat

doi:doi:10.11648/j.ajam.20170504.14

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Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses

Ubon Akpan Abasiekwere, Edwin Frank Nsien, Imoh Udo Moffat

Published in American Journal of Applied Mathematics (Volume 5, Issue 4)

Received: 20 October 2016 Accepted: 14 November 2016 Published: 24 August 2017

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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.

Published in	American Journal of Applied Mathematics (Volume 5, Issue 4)
DOI	10.11648/j.ajam.20170504.14
Page(s)	119-123
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Bounded, Oscillations, Second-order, Neutral, Delay, Impulsive, Differential Equation

References

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APA Style

Ubon Akpan Abasiekwere, Edwin Frank Nsien, Imoh Udo Moffat. (2017). Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses. American Journal of Applied Mathematics, 5(4), 119-123. https://doi.org/10.11648/j.ajam.20170504.14

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ACS Style

Ubon Akpan Abasiekwere; Edwin Frank Nsien; Imoh Udo Moffat. Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses. Am. J. Appl. Math. 2017, 5(4), 119-123. doi: 10.11648/j.ajam.20170504.14

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AMA Style

Ubon Akpan Abasiekwere, Edwin Frank Nsien, Imoh Udo Moffat. Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses. Am J Appl Math. 2017;5(4):119-123. doi: 10.11648/j.ajam.20170504.14

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@article{10.11648/j.ajam.20170504.14,
  author = {Ubon Akpan Abasiekwere and Edwin Frank Nsien and Imoh Udo Moffat},
  title = {Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {4},
  pages = {119-123},
  doi = {10.11648/j.ajam.20170504.14},
  url = {https://doi.org/10.11648/j.ajam.20170504.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170504.14},
  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.},
 year = {2017}
}

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TY  - JOUR
T1  - Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses
AU  - Ubon Akpan Abasiekwere
AU  - Edwin Frank Nsien
AU  - Imoh Udo Moffat
Y1  - 2017/08/24
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170504.14
DO  - 10.11648/j.ajam.20170504.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 119
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PB  - Science Publishing Group
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UR  - https://doi.org/10.11648/j.ajam.20170504.14
AB  - 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.
VL  - 5
IS  - 4
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Author Information

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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APA Style

Ubon Akpan Abasiekwere, Edwin Frank Nsien, Imoh Udo Moffat. (2017). Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses. American Journal of Applied Mathematics, 5(4), 119-123. https://doi.org/10.11648/j.ajam.20170504.14

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ACS Style

Ubon Akpan Abasiekwere; Edwin Frank Nsien; Imoh Udo Moffat. Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses. Am. J. Appl. Math. 2017, 5(4), 119-123. doi: 10.11648/j.ajam.20170504.14

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AMA Style

Ubon Akpan Abasiekwere, Edwin Frank Nsien, Imoh Udo Moffat. Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses. Am J Appl Math. 2017;5(4):119-123. doi: 10.11648/j.ajam.20170504.14

Copy | Download

@article{10.11648/j.ajam.20170504.14,
  author = {Ubon Akpan Abasiekwere and Edwin Frank Nsien and Imoh Udo Moffat},
  title = {Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses},
  journal = {American Journal of Applied Mathematics},
  volume = {5},
  number = {4},
  pages = {119-123},
  doi = {10.11648/j.ajam.20170504.14},
  url = {https://doi.org/10.11648/j.ajam.20170504.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20170504.14},
  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.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Oscillation Conditions for a Type of Second Order Neutral Differential Equations with Impulses
AU  - Ubon Akpan Abasiekwere
AU  - Edwin Frank Nsien
AU  - Imoh Udo Moffat
Y1  - 2017/08/24
PY  - 2017
N1  - https://doi.org/10.11648/j.ajam.20170504.14
DO  - 10.11648/j.ajam.20170504.14
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 119
EP  - 123
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20170504.14
AB  - 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.
VL  - 5
IS  - 4
ER  -

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