7 citations · 21 across the 18 of their papers we have counts for
21 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…
From formal to actual Puiseux series solutions of algebraic differential equations of first order
Vladimir Dragovic, Renat Gontsov, Irina Goryuchkina
The existence, uniqueness and convergence of formal Puiseux series solutions of non-autonomous algebraic differential equations of first order at a nonsingular point of the equatio…
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…