Second Order Nonlinear Differential Equations Equivalent To Linear Differential Equations
Second order nonlinear differential equations equivalent to linear differential equations.
Similarity and rescaling.
Smooth Gevrey normal forms of vector fields near a fixed point
We study germs of smooth vector fields in a neighborhood of a fixed point having an hyperbolic linear part at this point. It is well known that the “small divisors” are invisible either for the smooth linearization or normal form problem. We prove that this is completely different in the smooth Gevrey category. We prove that a germ of smooth -Gevrey vector field with an hyperbolic linear part admits a smooth -Gevrey transformation to a smooth -Gevrey normal form. The Gevrey order depends on...
Smooth linearization of centres
Smoothness as an invariant property of coefficients of linear differential equations
Solving an inverse Sturm-Liouville problem by a Lie-group method.
Some oscillatory properties of the perturbed linear differential equations of order
In this paper there are generalized some results on oscillatory properties of the binomial linear differential equations of order ) for perturbed iterative linear differential equations of the same order.
Some problems concerning the equivalences of two systems of differential equations
Some properties of linear homogeneous transformation of independent variable in ordinary differential linear equations
Some properties of third order differential operators
Consider the third order differential operator given by and the related linear differential equation . We study the relations between , its adjoint operator, the canonical representation of , the operator obtained by a cyclic permutation of coefficients , , in and the relations between the corresponding equations. We give the commutative diagrams for such equations and show some applications (oscillation, property A).
Special dispersions of the second order linear differential equations of a finite type special and their relation to the Kummer's transformation problem
Stationary groups of linear differential equations
Sur les blocs des équations différentielles linéaires du deuxième ordre et leurs transformations
Sur un théorème de Dulac
Nous considérons les champs de vecteurs analytiques de de partie linéaire diagonale non nulle et dont les valeurs propres vérifient des relations de résonances toutes engendrées par une seule relation pour un certain vecteur non nul. Nous montrons que, dans un système de coordonnées locales holomorphes au voisinages de , de tels champs de vecteurs se “mettent" sous une forme normale partielle, tout en exhibant des variétés invariantes, si l’on fait une hypothèse de petits diviseurs diophantiens....
Symmetries and solvability of linear differential equations.
The canonical form theorem, applied to a certain group of symmetry transformations of certain Fuchsian equations, leads automatically to the integration of them. The result can be extended to any n-order differential equation possesing a certain pointlike group of symmetries with a maximal abelian Lie-subgroup of order c.