International Journal of Nonlinear Analysis and Applications

Oscillation and asymptotic behavior of third-order semi-canonical difference equations with positive and negative terms

Document Type : Research Paper

Authors

1 Department of Mathematics, Periyar University, Salem 636011, Tamilnadu, India

2 Department of Mathematics, Periyar University College of Arts and Science, Pappireddipatti - 636905, Tamilnadu, India

3 Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai - 600 005, India

Abstract

This paper deals with the oscillatory and asymptotic properties of third-order semi-canonical difference equations with positive and negative terms of the form
$$\Delta\left(\varphi(\ell)\Delta\left(\psi(\ell)\Delta \mu(\ell) \right) \right)+\xi(\ell)f(\mu(\sigma(\ell)))-\chi(\ell)g(\mu(\tau(\ell)))=0.$$
Using a canonical transformation technique, we offer new criteria which imply that the solutions of the studied equation are almost oscillatory. Some examples are provided to support our results.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 1
January 2023
Pages 2519-2527
  • Receive Date: 28 February 2022
  • Revise Date: 08 September 2022
  • Accept Date: 29 December 2022