Stability criteria for certain second-order delay differential equations with mixed coefficients

In this paper, we study asymptotic stability of the zero solution of the second-order linear delay differential equation:y″(t)=p1y′(t)+p2y′(t−τ)+q1y(t)+q2y(t−τ),where p1, p2, q1, and q2 are constants with p1p2⩾0 and q1q2<0. Here τ>0 is a constant. In proving our results we make use of Pontryaginʹs theory of quasi-polynomials.