Further results on stability criteria for certain second-order delay differential equations with mixed coefficients

Further results on stability criteria for certain second-order...

Abstract

This work investigates the asymptotic stability of the trivial solution of the second-order linear delay differential equation
$$y''(t)=p_1y'(t)+p_2y'(t-\tau)+q_1y(t)+q_2y(t-\tau),$$ where $\tau>0,p_1,p_2,q_1,q_2$ are real numbers. By reducing the equation to a linear second-order ordinary differential equation with constant coefficients, sufficient conditions which guarantee the asymptotic stability of the trivial solution are obtained in a very simple form.