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.
|Journal||Electronic Journal of Differential Equations|
|State||Published - 1 Dec 2002|
- Absolute stability
- Aizerman-myshkis problem
- Input-output stability
- Nonlinear differential-delay equations in hilbert spaces