Oscillation of nonlinear neutral dynamic equations on time scales

G N Chhatria,John R Graef,Said R Grace

doi:10.1186/s42787-021-00131-w

Abstract

The authors present necessary and sufficient conditions for the oscillation of a class of second order non-linear neutral dynamic equations with non-positive neutral coefficients by using Krasnosel’skii’s fixed point theorem on time scales. The nonlinear function may be strongly sublinear or strongly superlinear.

Highlights

Neutral differential/difference equations find numerous applications in biology, engineering, economics, physics, neural networks, social sciences, etc
In the last few decades, many authors have focused their interest on the study of the oscillation of solutions of neutral differential/difference equations with deviating arguments, and in this regard, we refer the reader to the monographs of Agarwal et al [1, 2] and the papers [3, 7,8,9,10,11, 13,14,15, 22, 29]
For details on the theory of dynamic equations on time scales and its applications as well as for basic concepts and notations, we refer the reader to the works of Bohner and Peterson [5, 6]

Summary

Introduction

Neutral differential/difference equations find numerous applications in biology, engineering, economics, physics, neural networks, social sciences, etc (see, for example, [4, 12, 16]). In the last few decades, many authors have focused their interest on the study of the oscillation of solutions of neutral differential/difference equations with deviating arguments, and in this regard, we refer the reader to the monographs of Agarwal et al [1, 2] and the papers [3, 7,8,9,10,11, 13,14,15, 22, 29]. For details on the theory of dynamic equations on time scales and its applications as well as for basic concepts and notations, we refer the reader to the works of Bohner and Peterson [5, 6]. There are comparatively few papers concerned with the oscillation of equations with nonpositive neutral coefficients; for example, see [7, 14, 18, 20, 28]

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Discussion

Conclusion