Title: Riccati technique and oscillation of third order difference equations with impulse

Authors: G.N. Chhatria; A.K. Tripathy

Addresses: Department of Mathematics, Sambalpur University, Sambalpur – 768019, India ' Department of Mathematics, Sambalpur University, Sambalpur – 768019, India

Abstract: The subject of this discussion is the third order difference equations with fixed moments of impulsive effect. The goal of this paper is to establish the oscillatory behaviour of the aforementioned impulsive difference equations using the Riccati transformation approach along with some inequalities. We do not employ the monotonic properties of nonoscillatory solutions as we did in most of the prior results. The results obtained are new, and they generalise or extend previous research. In addition, we provide two illustrative examples to demonstrate that the findings in this work are easily verifiable. Finally, in the concluding remarks, we provide some insight on possible extensions of the examined topic.

Keywords: oscillation; nonoscillation; impulsive difference equation; Riccati transformation.

DOI: 10.1504/IJDSDE.2023.135021

International Journal of Dynamical Systems and Differential Equations, 2023 Vol.13 No.3, pp.209 - 217

Received: 12 Dec 2021
Received in revised form: 20 Mar 2023
Accepted: 05 Apr 2023
Published online: 27 Nov 2023 *

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