On the -boundedness of solutions for products of quasi-integro differential equations.
On the number of positive solutions of singularly perturbed 1D nonlinear Schrödinger equations
We study singularly perturbed 1D nonlinear Schrödinger equations (1.1). When has multiple critical points, (1.1) has a wide variety of positive solutions for small and the number of positive solutions increases to as . We give an estimate of the number of positive solutions whose growth order depends on the number of local maxima of . Envelope functions or equivalently adiabatic profiles of high frequency solutions play an important role in the proof.
On the order reduction of optimal control systems
On Tykhonov's theorem for convergence of solutions of slow and fast systems.
Order results for Rosenbrock type methods on classes of stiff equations.
Parameter-uniform fitted operator B-spline collocation method for self-adjoint singularly perturbed two-point boundary value problems.
Periodic solutions to a singular abstract differential equation
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...
Power bounded and exponentially bounded matrices
The paper gives a new characterization of eigenprojections, which is then used to obtain a spectral decomposition for the power bounded and exponentially bounded matrices. The applications include series and integral representations of the Drazin inverse, and investigation of the asymptotic behaviour of the solutions of singular and singularly perturbed differential equations. An example is given of localized travelling waves for a system of conservation laws.
Quasilinear and quadratic singularly perturbed Neumann's problem
The problem of existence and asymptotic behaviour of solutions of the quasilinear and quadratic singularly perturbed Neumann's problem as a small parameter at the highest derivative tends to zero is studied.
Quasilinear and quadratic singularly perturbed periodic boundary value problem
The problem of existence and asymptotic behavior of solutions of the quasilinear and quadratic singularly perturbed periodic boundary value problem as a small parameter at highest derivative tends to zero is studied.
Regular and singular perturbations of upper semicontinuous differential inclusions.
Résurgence paramétrique et exponentielle petitesse de l'écart des séparatrices du pendule rapidement forcé
Henri Poincaré avait déjà remarqué que les variétés stable et instable du pendule perturbé, défini par l’hamiltonienne coïncident pas lorsque que le paramètre n’est pas nul, mais qu’on peut leur associer un même développement formel divergent en puissance de . Cette divergence est ici analysée au moyen de la récente théorie de la résurgence, et du calcul étranger qui permet de trouver un équivalent asymptotique de l’écart des deux variétés pour tendant vers zéro - du moins cela est-il montré...
Robust monotone iterates for nonlinear singularly perturbed boundary value problems.
Singular perturbation for nonlinear boundary-value problems.
Singular perturbations for systems of differential inclusions
We study a system of two differential inclusions such that there is a singular perturbation in the second one. We state new convergence results of solutions under assumptions concerning contingent derivative of the perturbed inclusion. These results state that there exists at least one family of solutions which converges to some solution of the reduced system. We extend this result to perturbed systems with state constraints.
Singular perturbations of ordinary differential equations in Colombeau spaces
Singularité analytique et perturbation singulière en dimension 2
Singularly Perturbed Finite Element Methods.
Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions.