Asymptotische Formeln für die Lösungnen der Differentialgleichung
Bernstein classes
One of the classical Bernstein inequalities compares the maxima of a polynomial of a given degree on the interval [-1,1] and on the ellipse in the complex plane with the focuses -1, 1 and the semiaxes . We prove a similar inequality for a branch of an algebraic function of a given degree on the maximal disk of its regularity, with the explicitly given constant, depending on the degree only. In particular, this improves a recent inequality of Fefferman and Narasimhan and answers one of their questions....
Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems
In this paper we consider Bessel equations of the type , where A is an nn complex matrix and X(t) is an nm matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.
Caractérisation des dérivées logarithmiques
Champs lents-rapides complexes à une dimension lente
Ciertas propiedades de las ecuaciones diferenciales complejas con coeficients polinomicos
Contributions to the asymptotic behaviour of the equation with a complex-valued function
Correction and addition to my paper “The normal form and the stability of solutions of a system of differential equations in the complex domain”
Co-solutions of algebraic matrix equations and higher order singular regular boundary value problems
In this paper we obtain existence conditions and a closed form of the general solution of higher order singular regular boundary value problems. The approach is based on the concept of co-solution of algebraic matrix equations of polynomial type that permits the treatment of the problem without considering an extended first order system as it has been done in the known literature.
Croissance des solutions d'une équation différentielle homogène
Cycles évanescents d’une fonction de Liouville de type
On construit un transport transverse aux fibres d’une fonction multivaluée de type ( complexes), à l’origine de . Ce transport est unique à isotopie près. On en déduit l’existence de voisinages réguliers dans lesquels les fibres sont toutes difféomorphes (voire dans un cas quasi-homogène, analytiquement difféomorphes). On obtient également une généralisation de la notion de monodromie. On calcule enfin l’homologie évanescente de la fibre-type, en précisant le gradué qui lui est associé.
Das Existenzproblem multivalenter Lösungen bei Differentialgleichungen.
Diagonalization and rationalization of algebraic Laurent series
We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is an algebraic power series of degree at most and height at most , where is an effective constant that only depends on...
Die allgemeine Lösung einer zylindrischen Differentialgleichung vierter Ordnung nullten Parameterwertes
Diferenciální rovnice v komplexním oboru [Book]
Diferenciální rovnice v reálném oboru [Book]
Diskonjugierte Differentialgleichungen 2. Ordnung im Komplexen.
Diskonjugiertheit und k-Diskonjugiertheit von w(n) + f(x)w = 0 bei komplexwertigem f.
Diskonjugovaná a nekritická komplexná diferenciálna rovnica
Domaines de linearisation asymptotique pour des champs de vecteurs.