Exponent Estimation for Stable Solutions of a Certain Class of Differential-Difference Equations

For a differential-difference equation with a positive fundamental solution we obtain exponential stability conditions with exact estimates of the exponent and the coefficient of the exponential decay. These estimates are expressed in terms of the largest of two possible real roots of the characteristic function. We prove that one can obtain exact estimates for any solution by estimating the fundamental solution, taking into account the norm of the initial function. We establish two-sided estimates for the fundamental solution in the case, when equation parameters are given as intervals.