Canonical, Noncanonical, and Semicanonical Third Order Dynamic Equations on Time Scales

Abstract

The notion of third order semicanonical dynamic equations on time scales is introduced so that any third order equation is either in canonical, noncanonical, or semicanonical form. Then a technique for transforming each of the two types of semicanonical equations to an equation in canonical form is given. The end result is that oscillation and other asymptotic results for canonical equations can then be applied to obtain analogous results for semicanonical equations.