3 papers
math.CA2019
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…
math.CA2019
Linear Differential Systems with Small Coefficients: Various Types of Solvability and their Verification
Moulay A. Barkatou, Renat R. Gontsov
We study the problem of solvability of linear differential systems with small coefficients in the Liouvillian sense (or, by generalized quadratures). For a general system, this pro…
math.CA2018
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.