Oscillation of Solutions to Third-Order Nonlinear Neutral Dynamic Equations on Time Scales

Yang-Cong Qiu,Kuo-Shou Chiu,Said R Grace,Qingmin Liu,Irena Jadlovská

doi:10.3390/math10010086

Abstract

In this paper, we are concerned with the oscillation of solutions to a class of third-order nonlinear neutral dynamic equations on time scales. New oscillation criteria are presented by employing the Riccati transformation and integral averaging technique. Two examples are shown to illustrate the conclusions.

Highlights

We investigate the oscillation of solutions to a class of third-order halflinear dynamic equations with a nonpositive neutral coefficient
Therein, Džurina et al [3] and Santra et al [6] studied the oscillation of half-linear/Emden–Fowler delay differential equations with a sublinear neutral term, whereas the papers [1,4,5] were concerned with the asymptotics and oscillation of solutions to (1) and its modifications in the continuous case (i.e., T = R)
Data Availability Statement: Data sharing not applicable to this paper as no datasets were generated or analyzed during the current study

Summary

Introduction

We investigate the oscillation of solutions to a class of third-order halflinear dynamic equations with a nonpositive neutral coefficient. Therein, Džurina et al [3] and Santra et al [6] studied the oscillation of half-linear/Emden–Fowler delay differential equations with a sublinear neutral term, whereas the papers [1,4,5] were concerned with the asymptotics and oscillation of solutions to (1) and its modifications in the continuous case (i.e., T = R). There has been much attention to the study of oscillation of various classes of dynamic equations on time scales; see, for instance, the papers [13,14,15,16] concerning the analyses of. Two examples are presented to show the significance of the conclusions

Auxiliary Results

Main Results

Examples and Discussion