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