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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749


New Oscillation Conditions for Second Order Half-Linear Advanced Difference Equations

New Oscillation Conditions for Second Order Half-Linear Advanced Difference Equations

P. Dinakar
Department of Mathematics, Presidency College, University of Madras, Chennai - 600005, India.

S. Selvarangam
Department of Mathematics, Presidency College, University of Madras, Chennai - 600005, India.

E. Thandapani
Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai - 600005, India.

DOI https://dx.doi.org/10.33889/IJMEMS.2019.4.6-115

Received on March 25, 2019
  ;
Accepted on August 15, 2019

Abstract

This paper aims to establish adequate conditions that are intended for the oscillation of every solution of the second order advanced type half-linear difference equations with noncanonical form. Initially, we derive a sufficient condition that ensures all solutions of the studied equation are either oscillatory or tending to zero. Secondly, we obtain a criteria for the oscillation of all solutions of the studied equation. These criteria are obtained by using Riccati transformation and summation averaging method. The results established in this paper in essence complement, extend and enhance the existing outcomes recorded in the literature. The improvement of our main results are illustrated through three examples.

Keywords- Asymptotic behavior, Half-linear difference equation, Oscillation, Second order.

Citation

Dinakar, P., Selvarangam, S., & Thandapani, E. (2019). New Oscillation Conditions for Second Order Half-Linear Advanced Difference Equations. International Journal of Mathematical, Engineering and Management Sciences, 4(6), 1459-1470. https://dx.doi.org/10.33889/IJMEMS.2019.4.6-115.

Conflict of Interest

The authors confirm that this article contents have no conflict of interest.

Acknowledgements

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

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