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Subharmonic solutions of a nonconvex noncoercive hamiltonian system

Najeh Kallel, Mohsen Timoumi (2004)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper we study the existence of subharmonic solutions of the hamiltonian system J x ˙ + u * G ( t , u ( x ) ) = e ( t ) where u is a linear map, G is a C 1 -function and e is a continuous function.

Systèmes d'EDO invariants sous l'action de systèmes hyperboliques d'EDP

Denis Serre (1989)

Annales de l'institut Fourier

Lorsque tous les champs caractéristiques d’un système hyperbolique riche sont linéairement dégénérés, les opérateurs résolvants sont bien définis et opèrent sur l’ensemble des solutions de certains systèmes d’équations différentielles ordinaires. Celles-ci peuvent être implicites ou explicites. Dans le cas implicite, on montre que toutes les solutions sont presque-périodiques; de plus elles seront toutes périodiques pourvu que l’une d’entre elles le soit. Dans le cas explicite, on définit un opérateur...

Tame semiflows for piecewise linear vector fields

Daniel Panazzolo (2002)

Annales de l’institut Fourier

Let be a disjoint decomposition of n and let X be a vector field on n , defined to be linear on each cell of the decomposition . Under some natural assumptions, we show how to associate a semiflow to X and prove that such semiflow belongs to the o-minimal structure an , exp . In particular, when X is a continuous vector field and Γ is an invariant subset of X , our result implies that if Γ is non-spiralling then the Poincaré first return map associated Γ is also in an , exp .

The Conley index in Hilbert spaces and its applications

K. Gęba, M. Izydorek, A. Pruszko (1999)

Studia Mathematica

We present a generalization of the classical Conley index defined for flows on locally compact spaces to flows on an infinite-dimensional real Hilbert space H generated by vector fields of the form f: H → H, f(x) = Lx + K(x), where L: H → H is a bounded linear operator satisfying some technical assumptions and K is a completely continuous perturbation. Simple examples are presented to show how this new invariant can be applied in searching critical points of strongly indefinite functionals having...

The monotone iterative technique for periodic boundary value problems of second order impulsive differential equations

Eduardo Liz, Juan J. Nieto (1993)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we develop monotone iterative technique to obtain the extremal solutions of a second order periodic boundary value problem (PBVP) with impulsive effects. We present a maximum principle for ``impulsive functions'' and then we use it to develop the monotone iterative method. Finally, we consider the monotone iterates as orbits of a (discrete) dynamical system.

Currently displaying 501 – 520 of 587