On the convergence of formal Dulac series satisfying an algebraic ODE

Abstract

We propose a sufficient condition of the convergence of a Dulac series formally satisfying an algebraic ordinary differential equation (ODE). Such formal solutions of algebraic ODEs appear rather often, in particular, the third, fifth, and sixth Painlevé equations possess formal Dulac series solutions, whose convergence follows from the proposed sufficient condition.

arXiv comment13 pages

Cited by in corpus (2)

• On the convergence of an exotic formal series solution of an ODE
• On the convergence of exotic formal series solutions of an ODE. A proof by the implicit mapping theorem