Saddle Points and Multiple Solutions of Differential Equations.
Saddle-point problems in partial differential equations and applications to linear quadratic differential games
Saddle-shaped solutions of bistable diffusion equations in all of ℝ2m
Scalar boundary value problems on junctions of thin rods and plates
We derive asymptotic formulas for the solutions of the mixed boundary value problem for the Poisson equation on the union of a thin cylindrical plate and several thin cylindrical rods. One of the ends of each rod is set into a hole in the plate and the other one is supplied with the Dirichlet condition. The Neumann conditions are imposed on the whole remaining part of the boundary. Elements of the junction are assumed to have contrasting properties so that the small parameter, i.e. the relative...
Scalar differential invariants of symplectic Monge-Ampère equations
All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère equations with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. We also introduce a series of invariant differential forms and vector fields which allow us to construct numerous scalar differential invariants...
Scattering amplitude for the Schrödinger equation with strong magnetic field
In this note, we study the scattering amplitude for the Schrödinger equation with constant magnetic field. We consider the case where the strengh of the magnetic field goes to infinity and we discuss the competition between the magnetic and the electrostatic effects.
Scattering by two convex bodies
Scattering frequencies and Gevrey 3 singularities.
Scattering phases and density of states for exterior domains
Scattering problem for nonlinear Schrödinger equations
Scattering problems in a domain with small holes.
In this paper, we consider a family of scattering problems in perforated unbounded domains Ωε. We assume that the perforation is contained in a bounded region and that the holes have a ?critical? size. We study the asymptotic behaviour of the outgoing solutions of the steady-state scattering problem and we prove that an extra term appears in the limit equation. Finally, we obtain convergence results for scattering frequencies and solutions.
Scattering properties for a pair of Schrödinger type operators on cylindrical domains
Strong asymptotic completeness is shown for a pair of Schrödinger type operators on a cylindrical Lipschitz domain. A key ingredient is a limiting absorption principle valid in a scale of weighted (local) Sobolev spaces with respect to the uniform topology. The results are based on a refined version of Mourre’s method within the context of pseudo-selfadjoint operators.
Scattering Theory for Dirac Operators.
Scattering Theory for Elliptic Operators of Arbitrary Order
Scattering theory for one-dimensional step potentials
Scattering theory for the shape resonance model. I. Non-resonant energies
Scattering theory for the shape resonance model. II. Resonance scattering
Scattering theory in the weighted spaces for some Schrödinger equations
Scattering theory: Some old and new problems.
Scattering, transformations spectrales et équations d'évolution non linéaire II