On Properties of Third-Order Differential Equations via Comparison Principles

Abstract

The objective of this paper is to offer sufficient conditions for certain asymptotic properties of the third-order functional differential equation [𝑟(𝑡)[𝑥′(𝑡)]𝛾]+𝑝(𝑡)𝑥(𝜏(𝑡))=0, where studied equation is in a canonical form, that is, ∫∞𝑟−1/𝛾(𝑠)d𝑠=∞. Employing Trench theory of canonical operators, we deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones.