Stability theory for functional-differential equations

Author:
T. A. Burton

Journal:
Trans. Amer. Math. Soc. **255** (1979), 263-275

MSC:
Primary 34K20

DOI:
https://doi.org/10.1090/S0002-9947-1979-0542880-9

MathSciNet review:
542880

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Abstract: We consider a system of functional differential equations , together with a Liapunov functional with . Most classical results require that be bounded for bounded and that depend on only for where is a bounded function in order to obtain stability properties. We show that if there is a function whose derivative along is bounded above, then those requirements can be eliminated. The derivative of *H* may take both positive and negative values. This extends the classical theorem on uniform asymptotic stability, gives new results on asymptotic stability for unbounded delays and unbounded , and it improves the standard results on the location of limit sets for ordinary differential equations.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0542880-9

Keywords:
Stability,
Liapunov functions,
ordinary differential equations,
delay equations

Article copyright:
© Copyright 1979
American Mathematical Society