Oscillation Criteria for Third Order Neutral Generalized Difference Equations with Distributed Delay

P Venkata Mohan Reddy,Adem Kılıçman,M Maria Susai Manuel

doi:10.3390/sym11121501

Abstract

This paper aims to investigate the criteria of behavior of a certain type of third order neutral generalized difference equations with distributed delay. With the technique of generalized Riccati transformation and Philos-type method, we obtain criteria to ensure convergence and oscillatory solutions and suitable examples are provided to illustrate the main results.

Highlights

Difference equations and functional equations usually occur due to certain phenomena over time and play essential roles in the field of discrete dynamical systems [1]
An important and significant observation is that difference equations either appear in themselves and they can be used in Lie theory to get classes of exact solutions, or they can be obtained by discretizing the continuum equation in such a way to preserve the symmetries
We present new oscillation criteria for the generalized difference equation with distributed delay, which is new in the literature

Summary

Introduction

Difference equations and functional equations usually occur due to certain phenomena over time and play essential roles in the field of discrete dynamical systems [1]. Difference equations and their associated operators play a vital role as direct mathematical models of physical phenomena and provide powerful tools in numerical methods. Difference equations play an important role in Lie theory. An important and significant observation is that difference equations either appear in themselves and they can be used in Lie theory to get classes of exact solutions, or they can be obtained by discretizing the continuum equation in such a way to preserve the symmetries. For a detailed study on this aspect one can refer to [2,3,4,5]

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Conclusion