Formal and convergent power series solutions of singular partial differential equations

Abstract

A class of singular first-order partial differential equations is described for which an analogue of a theorem of M. Artin on the solutions of analytic equations holds: given any formal power series solution and any nonnegative integer v, a convergent power series solution may be found which agrees with the given formal solution up to all terms of order ⩽ v \leqslant v .