Stability of Solutions for Nonlinear Nonautonomous Differential-delay Equations in Hilbert Spaces

Abstract

We consider nonlinear non-autonomous differential-delay equations having separated linear and sublinear parts. We assume that the Green functions of the linear part is selfadjoint and positive definite to obtain solution estimates, explicit conditions for the absolute stability, and input-output stability. Moreover, it is shown that the suggested conditions characterize the equations that satisfy the generalized Aizerman-Myshkis hypothesis.