Asymptotics and Hille-Type Results for Dynamic Equations of Third Order with Deviating Arguments

Abstract

The aim of this paper is to deduce the asymptotic and Hille-type criteria of the dynamic equations of third order on time scales. Some of the presented results concern the sufficient condition for the oscillation of all solutions of third-order dynamical equations. Additionally, compared with the related contributions reported in the literature, the Hille-type oscillation criterion which is derived is superior for dynamic equations of third order. The symmetry plays a positive and influential role in determining the appropriate type of study for the qualitative behavior of solutions to dynamic equations. Some examples of Euler-type equations are included to demonstrate the finding.

Keywords

• asymptotic behavior
• Hille-type oscillation criteria
• Euler-type equation
• time scales
• dynamic equations