Periodic solutions in systems at resonances with small relay hysteresis
Perturbed linear rough differential equations
We study linear rough differential equations and we solve perturbed linear rough differential equations using the Duhamel principle. These results provide us with a key technical point to study the regularity of the differential of the Itô map in a subsequent article. Also, the notion of linear rough differential equations leads to consider multiplicative functionals with values in Banach algebras more general than tensor algebras and to consider extensions of classical results such as the Magnus...
Polynomial algebra of constants of the Lotka-Volterra system
Let k be a field of characteristic zero. We describe the kernel of any quadratic homogeneous derivation d:k[x,y,z] → k[x,y,z] of the form , called the Lotka-Volterra derivation, where A,B,C ∈ k.
Positive decreasing solutions of systems of second order singular differential equations.
Power series techniques for a special Schrödinger operator and related difference equations.
Practical method for solving differential equations and their systems bu means of Taylor series
Practice of operator relationships in symbolical calculus.
Principal solutions and transformations of linear Hamiltonian systems
Sufficient conditions are given which guarantee that the linear transformation converting a given linear Hamiltonian system into another system of the same form transforms principal (antiprincipal) solutions into principal (antiprincipal) solutions.
Problèmes de modules pour des équations différentielles non linéaires du premier ordre
Programming of differential equations with singularitiens of the type in using the extension to power series
Pseudo-integral of differential equations of the n-th order
Psi-series of quadratic vector fields on the plane.
Psi-series (i.e., logarithmic series) for the solutions of quadratic vector fields on the plane are considered. Its existence and convergence is studied, and an algorithm for the location of logarithmic singularities is developed. Moreover, the relationship between psi-series and non-integrability is stressed and in particular it is proved that quadratic systems with psi-series that are not Laurent series do not have an algebraic first integral. Besides, a criterion about non-existence of an analytic...