Stability criteria for certain third-order delay differential equations

In this paper, we study the asymptotic stability of the zero solution of third-order linear delay differential equations of the formy‴(t)=p1y″(t)+p2y″(t-τ)+q1y′(t)+q2y′(t-τ)+v1y(t)+v2y(t-τ),y‴(t)=p1y″(t)+p2y″(t-τ)+q1y′(t)+q2y′(t-τ)+v1y(t)+v2y(t-τ),where p1,p2,q1,q2,v1p1,p2,q1,q2,v1 and v2v2 are certain constants. Here τ>0τ>0 is a constant delay. In proving our results we make use of Pontryagin's theory for quasi-polynomials.