Stability of a third-order differential equation of retarded type (Q1316122)

The third-order differential equation of retarded type (1) \(\dddot x(t)=a \ddot x(t)+b \dot x(t)+cx(t) + f(x(t),\dot x(t-\tau))\) where \(a,b,c\) are negative constants, \(\tau>0\) is constant, \(f\) is continuously differentiable in all its arguments, is considered. Conditions are established under which the zero solution \(x(t)\) of (1) is asymptotically stable.