Oscillation of third order trinomial delay differential equations

摘要

The purpose of this paper is to study oscillation and asymptotic behavior of solutions to a third order linear delay differential equationy‴(t)+p(t)y′(t)+q(t)y(τ(t))=0.New comparison theorems deduce oscillation of the given third order delay differential equation via application of known oscillation criteria to associated first order delay differential equations or inequalities. Contrary to most known results, we establish oscillation of all solutions to a given delay differential equation. Conditions in all theorems are not difficult to verify; computer algebra systems can be efficiently used to assist the computations. Main results in the paper are illustrated with a number of examples.