Geometry of stochastic delay differential equations.
Geometry of third order ODE systems
We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of semisimple Lie algebras. We compute differential invariants up to degree 2 as application.
Germes de difféomorphismes et de champs de vecteurs en classe de différentiabilité finie
Pour tout triplet d’entiers tels que , se pose la question d’étudier les germes de difféomorphismes ou de champs de vecteurs sur , de classe , -déterminés en classe , c’est-à-dire respectivement conjugués ou équivalents en classe , à tout germe ayant la même classe et le même -jet. Cette question est abordée ici, avec quelque généralité en dimension 2 et pour les germes de champs de vecteurs de codimension 2, en dimension 3 et 4. Une conséquence de cette dernière étude est l’existence...
Ger-type and Hyers--Ulam stabilities for the first-order linear differential operators of entire functions.
Gestörte Verzweigung bei Potentialoperatoren.
Gevrey series of arithmetic type. I: Purity and duality theorems. (Séries Gevrey de type arithmétique. I: Théorèmes de pureté et de dualité.)
Gevrey series of arithmetic type. II: Transcendence without transcendence. (Séries Gevrey de type arithmétique. II: Transcendance sans transcendance.)
Gewöhnliche Differentialungsgleichungen mit quasimonoton waschsenden Funktionen.
Ghizzetti's theorem for piecewise continuous solutions.
Gleichmäßig asymptotische Stabilität stationäre Punkte bei Differential-Differenzengleichungen.
Gleichmäßig einschließende Diskretisierungsverfahren für schwach nichtlineare Randwertaufgaben.
Global asymptotic behavior of solutions of positively damped Liénard equations
Global asymptotic stability for half-linear differential systems with coefficients of indefinite sign
This paper is concerned with the global asymptotic stability of the zero solution of the half-linear differential system where , (), and for or . The coefficients are not assumed to be positive. This system includes the linear differential system with being a matrix as a special case. Our results are new even in the linear case (). Our results also answer the question whether the zero solution of the linear system is asymptotically stable even when Coppel’s condition does not hold...
Global asymptotic stability for plane polynomial flows
Global attractivity for a differential-difference population model.
Global attractivity of positive periodic solutions of delay differential equations with feedback control.
Global attractivity without stability for Liénard type systems.
Global Attractor for a Class of Parabolic Equations with Infinite Delay
We prove the existence of a compact connected global attractor for a class of abstract semilinear parabolic equations with infinite delay.
Global attractor of a differentiable autonomous system on the plane
We study the structure of a differentiable autonomous system on the plane with non-positive divergence outside a bounded set. It is shown that under certain conditions such a system has a global attractor. The main result here can be seen as an improvement of the results of Olech and Meisters in [7,9] concerning the global asymptotic stability conjecture of Markus and Yamabe and the Jacobian Conjecture.
Global attractors of non-autonomous quasi-homogeneous dynamical systems.