Properties of third-order nonlinear delay dynamic equations with positive and negative coefficients

Abstract

We study asymptotic properties of a class of third-order nonlinear delay dynamic equations with positive and negative coefficients on time scales. In this paper, we establish new results on asymptotic behavior of nonoscillatory and oscillatory solutions for the corresponding equations by making a comparison with suitable first-order dynamic equations. Finally, we offer an example to illustrate the feasibility of our results.

Oscillatory Properties for Second-Order Impulsive Neutral Dynamic Equations with Positive and Negative Coefficients on Time Scales

“…Moreover, dynamic equations with positive and negative coefficients have been of great interest. Many results on the oscillatory properties for dynamic equations with positive and negative coefficients have been obtained [11,12]. However, fewer papers are on the oscillation of impulsive neutral dynamic equations with positive and negative coefficients.…”