Algebraic foundations of the theory of singularly perturbed equations (Q1760967)

This short paper is related to the algebraic foundations of the theory of singular perturbations in the complex domain. It is shown, using the method of holomorphic regularization, that under some conditions the Cauchy problem \[ \epsilon\frac{dy}{dx}=f(x,y),\quad y(x_0,\epsilon)=y_0 \] has an unique solution that is pseudoholomorphic at the point \(\epsilon=0\).