The upper and lower solution method for nonlinear third-order three-point boundary value problem.
The use of fractional B-splines wavelets in multiterms fractional ordinary differential equations.
The use of Lyapunov functions in uniqueness and nonuniqueness theorems
The weak Cauchy problem for abstract differential equations
The Weinstein Conjecture in P X Cl.
The width of resonances for slowly varying perturbations of one-dimensional periodic Schrödinger operators
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...
The Yang-Mills gradient flow in four dimensions
Theorem of differential equations for Mikusinski operators.
Theorem On Differential Equations For Mikusinski Operators
Théorème de Paley-Wiener associé à un opérateur différentiel singulier sur
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
Theorems On Nonlinear Superpositions, III: Ordinary Differential Equations
Theorems on some families of fractional differential equations and their applications
We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for the vibration...
Théories de Galois différentielles et transcendance
On décrit des preuves galoisiennes des versions logarithmique et exponentielle de la conjecture de Schanuel, pour les variétés abéliennes sur un corps de fonctions.
Theory and numerics for multi-term periodic delay differential equations: small solutions and their detection.
Theory of completely integrable equations
Theory of linear abstract functional differential equations and applications.
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...