Exponential stability for autonomous linear functional differential equations with infinite retardations (Q1118743)

A nontrivial counterexample to Corduneanu and Lakshmikantham's problem is given on exponential stability of the fundamental matrix for a class of the most fundamental autonomous linear functional differential equations with infinite retardations. In abstract phase spaces, necessary and sufficient conditions are obtained for the exponential stability of the fundamental matrix of such general equations. It is shown that such stability is independent of the selection of phase spaces and it is proved theoretically that the answer of Corduneanu and Lakshmikantham's problem is false.