The Schauder-Tychonoff Fixed Point Theorem and Applications
The second term of the asymptotics of the monodromy map in case of two even edges of Newton diagram.
The semilinear Feng and FMV spectra.
The set of first-order differential equations with periodic or bounded solutions.
The objective of this note is the announcement of two results of Ambrosetti-Prodi type concerning the existence of periodic (respectively bounded) solutions of the first order differential equation x' = f (t,x).
The set of recurrent points of a continuous self-map on compact metric spaces and strong chaos
We discuss the existence of an uncountable strongly chaotic set of a continuous self-map on a compact metric space. It is proved that if a continuous self-map on a compact metric space has a regular shift invariant set then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.
The shadowing chain lemma for singular Hamiltonian systems involving strong forces
We consider a planar autonomous Hamiltonian system :q+∇V(q) = 0, where the potential V: ℝ2 {ζ→ ℝ has a single well of infinite depth at some point ζ and a strict global maximum 0at two distinct points a and b. Under a strong force condition around the singularity ζ we will prove a lemma on the existence and multiplicity of heteroclinic and homoclinic orbits - the shadowing chain lemma - via minimization of action integrals and using simple geometrical arguments.
The solution of the two-point boundary value problem for a nonlinear differential equation of the third order
The stability study of a plane engine
We study the dynamical properties of a plane engine vibrations modelled by a system of ODE.
The Sturm comparison theorem for -conjugate numbers
The sufficient condition of the asymptotic stability of two-dimensional linear systems
The topological behaviour of a diffeomorphism near a fixed point.
The uniqueness of the periodic solution for a class of differential equations.
The Weinstein Conjecture in P X Cl.
The XVI-th Hilbert problem about limit cycles
1. Introduction. The XVI-th Hilbert problem consists of two parts. The first part concerns the real algebraic geometry and asks about the topological properties of real algebraic curves and surfaces. The second part deals with polynomial planar vector fields and asks for the number and position of limit cycles. The progress in the solution of the first part of the problem is significant. The classification of algebraic curves in the projective plane was solved for degrees less than 8. Among general...
Théorèmes de finitude pour les variétés pfaffiennes
On introduit, dans ce travail, une hypothèse sur le spiralement d’une feuille d’un feuilletage analytique réel de codimension un (hypersurface pfaffienne). On en tire des résultats très généraux de finitude du type de Khovanskii. Des exemples précis montrent la généralité de ces hypersurfaces pfaffiennes. Une description complété des bouts de telles variétés en dimension trois est donnée.
Theorems of Bohr-Neugebauer-type for almost-periodic differential equations
Theory of rapid variation on time scales with applications to dynamic equations
In the first part of this paper we establish the theory of rapid variation on time scales, which corresponds to existing theory from continuous and discrete cases. We introduce two definitions of rapid variation on time scales. We will study their properties and then show the relation between them. In the second part of this paper, we establish necessary and sufficient conditions for all positive solutions of the second order half-linear dynamic equations on time scales to be rapidly varying. Note...
Three periodic solutions for an ordinary differential inclusion with two parameters
Applying a nonsmooth version of a three critical points theorem of Ricceri, we prove the existence of three periodic solutions for an ordinary differential inclusion depending on two parameters.
Three periodic solutions to an eigenvalue problem for a class of second-order Hamiltonian systems.
Three point value problem for third-order linear differential equation