Maillet--Malgrange type theorem for a formal Dulac series solution of an analytic ODE

A Maillet-Malgrange type theorem is proved for a Dulac series (in the general case, with complex exponents), which formally satisfies an analytical ordinary differential equation (ODE). This theorem allows to estimate the growth of the norms of the coefficients of such a series, that is, to determine its Gevrey order, and in the special case it provides a sufficient condition for the convergence of the series.