“…Then for each g(e) E " sufficiently small, which is K + 1 times continuously differentiable, there exists a solution X"(-, e), yL(., e), U"(', e) of (5) on 0<= '<--_ T/e, satisfying p"(0, e)= c(e). Moreover, XL(", e), Y'(', e), U'(", e) are K + 1 times continuously differentiable with respect to e, and satisfy decay condition (6) for some C > 0, > 0 and for all 0 <--<-T/e. In addition, if Xd ('), Y('), Ud (') represents the solution of (17), while for 1 <_-k _-< K, X('), Y('), U(') represents the solution of (18), then Our proof of Theorem 5.1 will follow by an appropriate interpretation of Hoppensteadt's Lemma 2 [8].…”