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Journal of Applied Mathematics and Computing

, Volume 59, Issue 1–2, pp 257–270 | Cite as

On oscillatory first order nonlinear neutral differential equations with nonlinear impulses

  • Shyam S. SantraEmail author
  • Arun K. Tripathy
Original Research

Abstract

In this work, we study the oscillatory behaviour of solutions of a class of first order impulsive neutral delay differential equations of the form
$$\begin{aligned} {\left\{ \begin{array}{ll} \bigl (y(t)-p(t)y(t-\tau )\bigr )' + q(t)G\bigl (y(t-\sigma )\bigr )=0,\;t\ne t_k,\;t \ge t_0 \\ y(t^+_k)=I_k\bigl (y(t_k)\bigr ), \;k \in {\mathbb {N}} \\ y(t^+_k-\tau )=I_k\bigl (y(t_k-\tau )\bigr ), \;k \in {\mathbb {N}} \end{array}\right. } \end{aligned}$$
for different ranges of the neutral coefficient p. Finally, two illustrative examples are included to show the effectiveness and feasibility of the main results.

Keywords

Oscillation Nonoscillation Neutral Impulsive differential equations Delay 

Mathematics Subject Classification

34K 

Notes

Acknowledgements

This work is supported by the Department of Science and Technology (DST), New Delhi, India, through the bank instruction Order No. DST/INSPIRE Fellowship/2014/140, dated Sept. 15, 2014.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.

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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.Department of MathematicsSambalpur UniversitySambalpurIndia

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