ﻻ يوجد ملخص باللغة العربية
Here we present some compliments to theorems of Gerard and Sibuya, on the convergence of multivariate formal power series solutions of nonlinear meromorphic Pfaffian systems. Their the most known results concern completely integrable systems with nondegenerate linear parts, whereas we consider some cases of non-integrability and degeneracy.
A sufficient condition for the convergence of a generalized formal power series solution to an algebraic $q$-difference equation is provided. The main result leans on a geometric property related to the semi-group of (complex) power exponents of such
We propose a sufficient condition of the convergence of a complex power type formal series of the form $varphi=sum_{k=1}^{infty}alpha_k(x^{{rm i}gamma}),x^k$, where $alpha_k$ are functions meromorphic at the origin and $gammain{mathbb R}setminus{0}$,
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 Pain
A sufficient condition of the convergence of an exotic formal series (a kind of power series with complex exponents) solution to an ODE of a general form is proposed.
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.