Zobrazeno 1 - 10
of 47
pro vyhledávání: '"Goryuchkina, Irina"'
Autor:
Gontsov, Renat, Goryuchkina, Irina
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 approaches to study them is, firstly, to find formal solutions (that is,
Externí odkaz:
http://arxiv.org/abs/2412.00778
The question of the convergence of generalized formal power series (with complex power exponents) solutions of $q$-difference equations is studied in the situation where the small divisors phenomenon arises; a sufficient condition of convergence gene
Externí odkaz:
http://arxiv.org/abs/2209.09365
Autor:
Gontsov, Renat, Goryuchkina, Irina
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 form and properties of the functional coefficients of such a series are
Externí odkaz:
http://arxiv.org/abs/2111.07159
Autor:
Gontsov, Renat, Goryuchkina, Irina
Publikováno v:
In Journal of Symbolic Computation May-June 2025 128
Publikováno v:
Aequat. Math., 2022, V. 96(3), 579-597
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
Externí odkaz:
http://arxiv.org/abs/2011.06384
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 equation is studied, including the case where the celebrated Painleve theorem
Externí odkaz:
http://arxiv.org/abs/2008.02982
Autor:
Dragovic, Vladimir, Goryuchkina, Irina
Here, we study the genesis and evolution of geometric ideas and techniques in investigations of movable singularities of algebraic ordinary differential equations. This leads us to the work of Mihailo Petrovic on algebraic differential equations and
Externí odkaz:
http://arxiv.org/abs/1908.03644
Autor:
Gontsov, Renat, Goryuchkina, Irina
Publikováno v:
"On the convergence of formal exotic series solutions of an ODE", Comput. Methods Funct. Theory, 2020, V. 20(2), 279-295
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 $\gamma\in{\mathbb R}\s
Externí odkaz:
http://arxiv.org/abs/1906.06716
Autor:
Gontsov, Renat, Goryuchkina, Irina
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.
Externí odkaz:
http://arxiv.org/abs/1812.11814
Autor:
Gontsov, Renat, Goryuchkina, Irina
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 non
Externí odkaz:
http://arxiv.org/abs/1808.01521