Abstract
Abstract : The problem of determining the asymptotic nature of the solution of linear differential-difference equations of the form x'(t) = A(t)x(t) + B(t)x(t-1), where the coefficients A(t) and B(t) possess asymptotic series expansions has previously been treated only under quite special conditions and by quite complicated methods. The purpose of this paper is to present a new technique which will yield more comprehensive results. To illustrate the method, unhindered by analytic details, the author considers the scalar version of the foregoing equation and treat only the asymptotic series of the solution associated with the characteristic root of the largest real part.
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