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Oscillation of Second Order Neutral Type Emden–Fowler Delay Difference Equations

  • Dinakar Ponnuraj
  • Selvarangam Srinivasan
  • Thandapani EthirajuEmail author
Original Paper
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Abstract

In this paper, the authors using summation averaging method and an inequality present some new oscillation criteria for the second order neutral type Emden–Fowler delay difference equation
$$\begin{aligned} \varDelta (f_i |\varDelta \chi _i|^{\alpha -1} \varDelta \chi _i) + g_i |\psi _{i-l}|^{\beta -1} \psi _{i-l} = 0, \quad i \ge i_0 >0, \end{aligned}$$
(1)
where \(\chi _i = \psi _i + h_i \psi _{i-k}, \; \alpha > 0\) and \(\beta > 0\). The obtained results improve and extend some known results recorded in the literature. Examples illustrating the significance of our results are provided.

Keywords

Emden–Fowler difference equation Oscillation Second-order 

Mathematics Subject Classification

39A10 
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Notes

Acknowledgements

The authors thank the reviewers for his/her valuable suggestions and corrections that improved the contents of the paper.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

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© Springer Nature India Private Limited 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Presidency CollegeUniversity of MadrasChennaiIndia
  2. 2.Ramanujan Institute for Advanced Study in MathematicsUniversity of MadrasChennaiIndia

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