An extension of the Alekseev variation of constant formula for neutral nonlinear perturbed equation with an application to the relative asymptotic equivalence
The authors consider nonlinear neutral functional differential equations and certain perturbations of these and the relative asymptotic equivalence between solutions. Sufficient conditions, using an Alekseev- type variation of constants formula, are given for such relative asymptotic equivalence. This paper contains rather detailed technicalities and assumes a fair amount of familiarity with neutral functional equation theory and notation. The reviewer also noted a number of inconsistences in it; for example, in the definition of D(t,\(\phi)\), it seems the lower limit of integration should be \(\sigma\)-r rather than -r; also in the remark following Lemma 2.1, D(t,\(\phi)\) seems to be assumed independent of t; in fact, this is the case in the example discussed in the last section of this paper.
nonlinear neutral functional differential equations
Alekseev-type variation of constants formula
scientific article; zbMATH DE number 3996189