On Stability With Derivative of a Class of Differential Equations of Neutral Type

Abstract

We consider an important class of differential-difference equations of neutral type, for which we study the asymptotic properties of a solution. We present necessary and sufficient conditions of exponential stability. The conditions have a geometric form of a region in the parameter space. The behavior of a solution at the boundaries of the region is analyzed separately. The loss of stability on the boundary can occur in various ways, namely through the appearance of stationary solutions, and through the appearance of periodic modes. Along with the asymptotic properties of a solution, we study analogous properties of its derivative.