On the asymptotic expansion of the Airy function
Si prova una nuova formula di rappresentazione per la famosa funzione di Airy. Ne viene data applicazione per la determinazione di certi bounds significativi per la funzione stessa.
On the behaviour of solutions of the differential equations
On the existence of solutions of the singular Cauchy problem for systems of differential equations not solved with respect to the derivatives.
On the functional integrability and asymptotic behaviours of a certain differential equation with delay
On the Liouville-type transformation for differential systems
On the step-type contrast structure of a second-order semilinear differential equation with integral boundary conditions.
Oscillating rivers. (Fleuves oscillants.)
Oscillation and asymptotic properties of strongly sublinear differential equations with deviating arguments
Oscillation criteria for certain nonlinear fourth order equations.
Oscillations of superlinear differential equations with deviating arguments
Oscillatory and asymptotic properties of third and fourth order linear differential equations
Overstability and resonance
We consider a singularity perturbed nonlinear differential equation which we suppose real analytic for near some interval and small , . We furthermore suppose that 0 is a turning point, namely that is positive if . We prove that the existence of nicely behaved (as ) local (at ) or global, real analytic or solutions is equivalent to the existence of a formal series solution with analytic at . The main tool of a proof is a new “principle of analytic continuation” for such “overstable” solutions....
Periodical solutions of some differential equations with small parameter
Perturbation singulière en dimension trois : canards en un point pseudo-singulier nœud
On étudie les systèmes différentiels singulièrement perturbés de dimension 3 du typeoù , , sont analytiques quelconques. Les travaux antérieurs étudiaient les points réguliers où la surface lente est transverse au champ rapide vertical. C’est le domaine d’application du théorème de Tikhonov. Dans d’autres travaux antérieurs, on étudiait les singularités de certains types : plis et fronces de la surface lente, ainsi que certaines singularités plus compliquées, analogues aux points tournants...
Polynomial expansiveness and admissibility of weighted Lebesgue spaces
The paper investigates the interaction between the notions of expansiveness and admissibility. We consider a polynomially bounded discrete evolution family and define an admissibility notion via the solvability of an associated difference equation. Using the admissibility of weighted Lebesgue spaces of sequences, we give a characterization of discrete evolution families which are polynomially expansive and also those which are expansive in the ordinary sense. Thereafter, we apply the main results...
Problème du chasseur au trosième ordre.
Prolungamento dellacurva integrale del sistema di equazioni differenziali sull’insieme singolare. Teoria e applicazioni
Recent results on the separatrix splitting for the standard map
Rectification d’une formule dans l’article: „Les développements asymptotiques des solutions de l’équation ‟
Regularity, nonoscillation and asymptotic behaviour of solutions of second order linear equations.