Electron. J. Diff. Eqns., Vol. 2002(2002), No. 94, pp. 1-15.

Stability of solutions for nonlinear nonautonomous differential-delay equations in Hilbert spaces

Michael I. Gil'

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.

Submitted September 19, 2002. Published October 31, 2002.
Math Subject Classifications: 34G20, 34K20, 34K99.
Key Words: nonlinear differential-delay equations in Hilbert spaces, absolute stability, input-output stability, Aizerman-Myshkis problem.

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Michael I. Gil'
Department of Mathematics
Ben Gurion University of the Negev
P.0. Box 653, Beer-Sheva 84105, Israel
E-mail: gilmi@black.bgu.ac.il

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