On the holomorphic regularization of singularly perturbed systems of differential equations (Q1682910)

The paper deals with a holomorphic regularization based on Lomov's regularization method for the singularly perturbed system \[ \varepsilon y'=f(t,y),\;t\in[0,T],\;y\in\mathbb{R}^k, \;y(0,\varepsilon)=y_0. \] The original nonlinear problem is reduced to a linear problem studied as a regular one by using the asymptotic expansion techniques, and subsequently, the implicit function theorem is applied to show that the solution of the Cauchy problem under consideration is pseudo-holomorphic in the global sense.