Sufficient and necessary condition for the permanence of periodic predator-prey system.
Sul problema della biforcazione generalizzata di Hopf per sistemi periodici
Sur le calcul de la partie principale d'un tore de bifurcation pour un système différentiel périodique
Sur l'existence d'une solution périodique d'une équation différentielle à paramètre retardé et à petit paramètre
Sur l'existence d'une solution périodique d'une équation différentielle du premier ordre avec le paramètre retardeé
Systèmes d'EDO invariants sous l'action de systèmes hyperboliques d'EDP
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
Let be a disjoint decomposition of and let be a vector field on , defined to be linear on each cell of the decomposition . Under some natural assumptions, we show how to associate a semiflow to and prove that such semiflow belongs to the o-minimal structure . In particular, when is a continuous vector field and is an invariant subset of , our result implies that if is non-spiralling then the Poincaré first return map associated is also in .
The characteristic multipliers of a block and of an inverse block of second-order linear differential equations with -periodic coefficients
The Conley index in Hilbert spaces and its applications
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 existence of periodic solutions of an autonomous second order non-linear differential equation
The first kind periodic solutions of differential equations of the second order
The first, the second, and the third Liouville formula and periodical solutions of linear differential equation of the second order
The method of lower and upper solutions for th-order periodic boundary value problems.
The minimal period problem of classical hamiltonian systems with even potentials
The monotone iterative technique for periodic boundary value problems of second order impulsive differential equations
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.
The Number and Linking of Periodic Solutions of Periodic Systems.
The period function near a polycycle with two semi-hyperbolic vertices
The period of oscillations in non-linear systems
The periodic Ambrosetti-Prodi problem for nonlinear perturbations of the p-Laplacian
We prove an Ambrosetti–Prodi type result for the periodic solutions of the equation , when is arbitrary and or when . The proof uses upper and lower solutions and the Leray–Schauder degree.
The periodic problem for semilinear differential inclusions in Banach spaces
Sufficient conditions on the existence of periodic solutions for semilinear differential inclusions are given in general Banach space. In our approach we apply the technique of the translation operator along trajectories. Due to recent results it is possible to show that this operator is a so-called decomposable map and thus admissible for certain fixed point index theories for set-valued maps. Compactness conditions are formulated in terms of the Hausdorff measure of noncompactness.