Singular limits for a 4-dimensional semilinear elliptic problem with exponential nonlinearity
Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances
We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrödinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of , and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually, we...
Stability and instability of equilibria on singular domains
We show existence of nonconstant stable equilibria for the Neumann reaction-diffusion problem on domains with fractures inside. We also show that the stability properties of all hyperbolic equilibria remain unchanged under domain perturbation in a quite general sense, covered by the theory of Mosco convergence.
Stationary radial solutions for a quasilinear Cahn-Hilliard model in space dimensions.
Sur un théorème de point critique et application à un problème de non-résonance entre deux valeurs propres du -laplacien