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Stability for retarded functional differential equations. (English) Zbl 1164.34530
Summary: It is known that retarded functional differential equations can be regarded as Banach-space-valued generalized ordinary differential equations (GODEs). Here, some stability concepts for retarded functional differential equations are introduced and discussed using known stability results for GODEs. Upon proving the equivalence of the different concepts of stability considered, converse Lyapunov theorems for a very wide class of retarded functional differential equations are obtained by means of the correspondence of this class to GODEs.

MSC:
34K20Stability theory of functional-differential equations
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