Techniques of the differential subordination for domains bounded by conic sections.
The analytic Carathéodory conjecture.
The equation in when is quasi-invertible
The existence and the uniqueness of distributional solutions of some systems of non-linear differential equations
The formal solution of Mikusiński operational differential equations with variable coefficients.
The moving frames for differential equations. I. The change of independent variable
The article concerns the symmetries of differential equations with short digressions to the underdetermined case and the relevant differential equations with delay. It may be regarded as an introduction into the method of moving frames relieved of the geometrical aspects: the stress is made on the technique of calculations employing only the most fundamental properties of differential forms. The present Part I is devoted to a single ordinary differential equation subjected to the change of the independent...
The moving frames for differential equations. II. Underdetermined and functional equations
Continuing the idea of Part I, we deal with more involved pseudogroup of transformations , , applied to the first order differential equations including the underdetermined case (i.e. the Monge equation ) and certain differential equations with deviation (if is substituted). Our aim is to determine complete families of invariants resolving the equivalence problem and to clarify the largest possible symmetries. Together with Part I, this article may be regarded as an introduction into the...
The numerical method for solving differential equations of Lane-Emden type by Padé approximation.
The -product approach for linear ODEs: A numerical study of the scalar case
Solving systems of non-autonomous ordinary differential equations (ODE) is a crucial and often challenging problem. Recently a new approach was introduced based on a generalization of the Volterra composition. In this work, we explain the main ideas at the core of this approach in the simpler setting of a scalar ODE. Understanding the scalar case is fundamental since the method can be straightforwardly extended to the more challenging problem of systems of ODEs. Numerical examples illustrate the...
To the definition of the global transformation in 2-dimensional linear spaces of continuous functions
To the theory of global transformation of the second order linear differential equations of finite type, special
Transformations of ordinary differential equations
The paper describes the general form of an ordinary differential equation of an order which allows a nontrivial global transformation consisting of the...