The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces
The Cauchy problem of the one dimensional Schrödinger equation with non-local potentials.
The distance between fixed points of some pairs of maps in Banach spaces and applications to differential systems
Let be a -contraction on a Banach space and let be an almost -contraction, i.e. sum of an -contraction with a continuous, bounded function which is less than in norm. According to the contraction principle, there is a unique element in for which If moreover there exists in with , then we will give estimates for Finally, we establish some inequalities related to the Cauchy problem.
The Perron product integral and generalized linear differential equations
The steepest descent dynamical system with control. Applications to constrained minimization
Let be a real Hilbert space, a convex function of class that we wish to minimize under the convex constraint . A classical approach consists in following the trajectories of the generalized steepest descent system (cf. Brézis [5]) applied to the non-smooth function . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function whose critical points coincide with and a control...
The steepest descent dynamical system with control. Applications to constrained minimization
Let H be a real Hilbert space, a convex function of class that we wish to minimize under the convex constraint S. A classical approach consists in following the trajectories of the generalized steepest descent system (cf. Brézis [CITE]) applied to the non-smooth function . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function whose critical points coincide with S and...
The use of Lyapunov functions in uniqueness and nonuniqueness theorems
The weak Cauchy problem for abstract differential equations
Topological transversality. Applications to initial-value problems
Transport equations with partially velocities
We prove the uniqueness of weak solutions for the Cauchy problem for a class of transport equations whose velocities are partially with bounded variation. Our result deals with the initial value problem where is the vector fieldwith a boundedness condition on the divergence of each vector field . This model was studied in the paper [LL] with a regularity assumption replacing our hypothesis. This settles partly a question raised in the paper [Am]. We examine the details of the argument of...
Tеоремы существования неотрицательных периодических решений конечных и счетных систем дифференциальных уравнений и теорема существования решений счетных систем дифференциальных уравнений
Über den Satz von Poincaré in der Störungstheorie Briot-Bouquetscher Differentialgleichungen.
Über die Beschränktheit und die Existenz von Lösungen der Differentialgleichung 4. Ordnung mit nacheilendem Argument
Über die Kategorie der Menge stetiger Funktionen, welche Differentialgleichungen ohne Eindeutigkeit bestimmen
Über eine Verallgemeinerung der Nicoletti-Aufgabe für Funktional-Differentialgleichungen mit voreilendem Argument.
Über einen Satz von Witte.
Über unendliche Systeme von gewöhnlichen Differentialgleichungen
Über verallgemeinerte Differentialgleichungen von Aczél-Jabotinsky im Komplexen. (Parameterabhängigkeit und holomorphe Fortsetzung von Integralen). (On generalized differential equations of Aczél-Jabotinsky in the complex domain. (Parameter-dependence and holomorphic continuation of integrals.)).
Un teorema di esistenza e di unicità per un'equazione differenziale non lineare
Une remarque sur le théorème de Jürgen Witte sur l'unicité de la solution de l'équation differentielle y' = f(x, y)