Characterising small solutions in delay differential equations through numerical approximations

The existence of small solutions, that is solutions that decay faster than any exponential, for linear time-dependent delay differential equations with bounded coefficients depends on specific properties of the coefficients. Although small solutions do not occur in the finite dimensional approximations of the delay differential equation we show that the existence of small solutions for delay differential equations can be predicted from the behaviour of the spectrum of the finite dimensional approximations. (C) 2002 Elsevier Science Inc. All rights reserved.