Analyticity with respect to a parameter of regular solutions of weakly nonlinear singularly perturbed problems

We consider a weakly nonlinear singular perturbed problem with right side independent of time. We show that the regularized asymptotic series obtained by Lomov's method are analytic with respect to the parameter and regularizing variables.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 393—398, March, 1990.