We propose a sufficient condition of the convergence of a generalized power series formally satisfying an algebraic (polynomial) ordinary differential equation. The proof is based on the majorant method.
The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular ones and pr
opose some criteria of solvability for systems whose (formal) exponents are sufficiently small.
