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
Three-dimensional cooperative irreducible systems with a first integral
Time averaging for functional differential equations.
Time averaging for ordinary differential equations and retarded functional differential equations.
Time delay in chemical exchange during an NMR pulse
Spin exchange with a time delay in NMR (nuclear magnetic resonance) was treated in a previous work. In the present work the idea is applied to a case where all magnetization components are relevant. The resulting DDE (delay differential equations) are formally solved by the Laplace transform. Then the stability of the system is studied using the real and imaginary parts of the determinant in the characteristic equation. Using typical parameter values for the DDE system, stability is shown for all...
To conjugacy functions of second order linear differential equations
To existence of the periodic solution of a third-order nonlinear differential equation
To the definition of the global transformation in 2-dimensional linear spaces of continuous functions
To the question of oscillation of solutions of two-dimensional differential systems with deviated arguments.
To the theory of central dispersions for the linear differential equations of a finite type-special
To the theory of global transformation of the second order linear differential equations of finite type, special
Topogical equivalence of monotone nonlinear nonautonomous differential equations