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Oscillation of Second Order Impulsive Neutral Difference Equations of Non-canonical Type

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Advances in Discrete Dynamical Systems, Difference Equations and Applications (ICDEA 2021)

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Abstract

In this article, necessary and sufficient conditions for the oscillation of a class of nonlinear second order neutral impulsive difference equations of the form:

$$\begin{aligned} {\left\{ \begin{array}{ll} \varDelta [a(n)\varDelta (x(n)+p(n)x(n -\tau ))] +q(n)F(x(n -\sigma ))=0,\, n\ne m_{j} \\ \underline{\varDelta }[a(m_j-1)\varDelta (x(m_j-1)+p(m_j-1)x(m_j-\tau -1))]\\ \qquad \qquad \qquad \qquad\quad+ r(m_j-1)F(x(m_j-\sigma -1))=0,\,j\in \mathbb {N} \end{array}\right. } \end{aligned}$$

have been discussed for \(p(n)\in (-1,0]\) with fixed moments of impulsive effect. Here, we assume that the nonlinear function is either strongly sublinear or strongly superliner. Some examples are given to illustrate our main results.

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Acknowledgement

The authors are thankful to the editor and anonymous referees for their careful reading of the manuscript and helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Sambalpur University, Sambalpur, 768019, India

    G. N. Chhatria & A. K. Tripathy

Authors
  1. G. N. Chhatria
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  2. A. K. Tripathy
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Correspondence to G. N. Chhatria .

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Editors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, TX, USA

    Saber Elaydi

  2. University of Rhode Island, Kingston, RI, USA

    Mustafa R. S. Kulenović

  3. University of Sarajevo, Sarajevo, Bosnia and Herzegovina

    Senada Kalabušić

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Chhatria, G.N., Tripathy, A.K. (2023). Oscillation of Second Order Impulsive Neutral Difference Equations of Non-canonical Type. In: Elaydi, S., Kulenović, M.R.S., Kalabušić, S. (eds) Advances in Discrete Dynamical Systems, Difference Equations and Applications. ICDEA 2021. Springer Proceedings in Mathematics & Statistics, vol 416. Springer, Cham. https://doi.org/10.1007/978-3-031-25225-9_8

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