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 form y ‴ ( t ) = p 1 y ″ ( t ) + p 2 y ″ ( t - τ ) + q 1 y ′ ( t ) + q 2 y ′ ( t - τ ) + v 1 y ( t ) + v 2 y ( t - τ ) , where p 1 , p 2 , q 1 , q 2 , v 1 and v 2 are certain constants. Here τ > 0 is a constant delay. In proving our results we make use of Pontryaginʹs theory for quasi-polynomials.