2 citations · 5 across the 9 of their papers we have counts for
11 papers
Convergence of (generalized) power series solutions of functional equations
Renat Gontsov, Irina Goryuchkina
Solutions of nonlinear functional equations are generally not expressed as a finite number of combinations and compositions of elementary and known special functions. One of the ap…
Small divisors in the problem of the convergence of generalized power series solutions of -difference equations
Renat Gontsov, Irina Goryuchkina, Alberto Lastra
The question of the convergence of generalized formal power series (with complex power exponents) solutions of -difference equations is studied in the situation where the small…
On the convergence of formal power-log series solutions of an algebraic ODE
Renat Gontsov, Irina Goryuchkina
We propose a sufficient condition of the convergence of a power-log series that formally satisfies an algebraic ordinary differential equation (ODE) of arbitrary order. A general f…
On the convergence of generalized power series solutions of -difference equations
Renat Gontsov, Irina Goryuchkina, Alberto Lastra
A sufficient condition for the convergence of a generalized formal power series solution to an algebraic -difference equation is provided. The main result leans on a geometric p…
On the convergence of exotic formal series solutions of an ODE. A proof by the implicit mapping theorem
Renat Gontsov, Irina Goryuchkina
We propose a sufficient condition of the convergence of a complex power type formal series of the form , where are functions mero…
On the convergence of an exotic formal series solution of an ODE
Renat Gontsov, Irina Goryuchkina
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.
A note on the convergence of multivariate formal power series solutions of meromorphic Pfaffian systems
Renat Gontsov, Irina Goryuchkina
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…
On the convergence of formal Dulac series satisfying an algebraic ODE
Irina Goryuchkina, Renat Gontsov
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 ODE…
The Maillet--Malgrange type theorem for generalized power series
Renat Gontsov, Irina Goryuchkina
There is proposed the Maillet--Malgrange type theorem for a generalized power series (having complex power exponents) formally satisfying an algebraic ordinary differential equatio…
On the convergence of generalized power series satisfying an algebraic ODE
Renat Gontsov, Irina Goryuchkina
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…
An analytic proof of the Malgrange-Sibuya theorem on the convergence of formal solutions of an ODE
R. R. Gontsov, I. V. Goryuchkina
We propose an analytic proof of the Malgrange-Sibuya theorem concerning a sufficient condition of the convergence of a formal power series satisfying an ordinary differential equat…