ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SOME RETARDED DIFFERENTIAL EQUATIONS

In an international conference on nonlinear systems and applications, 1976, S. R.Bernfeld and J. R. Haddock proposed a conjecture that each solution of a retarded equationx’（t） = -x（t） + x（t-r）tends to a constant as t→∞. It is the purpose of this paper to give a proof of the conjec-ture. In fact, we have proved the more general results, i.c., Theorems 1, 2 and 3 stated inSec. III.