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 |
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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. |
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Copyright © The Author(s), 2017. Published by Science Publishing Group |
Bounded, Oscillations, Second-order, Neutral, Delay, Impulsive, Differential Equation
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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
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
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
@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} }
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 -