ABSTRACT
Stability of the first and second order functional differential equations were intensively studied in last decade. Essentially less recent publications study third order delay equations. In this Chapter, assertions on the exponential stability of linear third order delay differential equations are obtained. Results are based on the idea of the Azbelev W-transform. Results are of the form: if all the roots of the characteristic equation of the third order ordinary differential equation have negative real parts and the delays in this equation are small enough, then the delay equation with the same coefficients is exponentially stable. The “smallness” of the delays is described through the coefficients of the third order delay equations.
