Abstract
This paper concerns asymptotic integration of nth order linear differential equations which are perturbations of equations having constant coefficients and which have zero as a characteristic number. When the unperturbed equation has no other purely imaginary characteristic number, Dunkel’s general result has been successively improved by Hartman and Wintner and by Prevatt. A generalization of Prevatt’s result is obtained when other purely imaginary characteristic numbers are present. It is also observed that results on integration by Laplace–Stieltjes transforms suggest some questions about asymptotic integration.
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