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

摘要

In this paper, we study asymptotic stability of the zero solution of the second-order linear delay differential equation: y″(t)=p_1y′(t)+p_2y′(t-τ)+q_1y(t)+q_2y(t-τ), where p_1, p_2, q_1, and q_2 are constants with p_1p_2≥0 and q_1q_2<0. Here τ>0 is a constant. In proving our results we make use of Pontryagin's theory of quasi-polynomials.