Integral criteria of oscillation for a third order linear differential equation
Si studia l'equivalenza asintotica fra le soluzioni di un sistema lineare e quelle di una perturbazione non lineare. Vengono date condizioni sufficienti per l'esistenza di un omeomorfìsmo fra le soluzioni limitate di tali sistemi.
Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.
* This investigation was supported by the Bulgarian Ministry of Science and Education under Grant MM-7.Sufficient conditions are obtained for the existence of local integral manifolds of autonomous systems of differential equations with impulses at fixed moments. In case of perturbations of the nonlinear part an estimate of the difference between the manifolds is obtained.
The problem of integrating factor for ordinary differential equations is investigated. Conditions are given which guarantee that each solution of is also a solution of where and .
On considère le problème de déterminer les solutions d’une équation différentielle ordinaire, dite de Risch sur une courbe algébrique. En fait une généralisation assez évidente de la méthode de Risch suffit mais elle nous permet de généraliser son algorithme d’intégration à toute extension élémentairement transcendante d’une extension algébrique des fonctions rationnelles.