We consider the cubic-quintic nonlinear Schrödinger equation of up to three space
dimensions. The cubic nonlinearity is thereby focusing while the quintic one is defocusing …

In this paper we first prove a general result about the uniqueness and non-degeneracy of
positive radial solutions to equations of the form Δ u+ g (u)= 0 Δ u+ g (u)= 0. Our result …

This article is concerned with the quasilinear Schr\" odinger equation\[\Delta u-\omega u+|
u|^{p-1} u+\delta\Delta (| u|^ 2) u= 0,\] where $\delta> 0$, $ N= 2$ and $ p> 1$ or $ N\ge3 …

We consider the nonlinear Schr\" odinger equation with a focusing cubic term and a
defocusing quintic nonlinearity in dimensions two and three. The core of this article is the …

Abstract We consider the Thomas–Fermi–Dirac–von Weizsäcker model for a system
composed of infinitely many nuclei placed on a periodic lattice and electrons with a periodic …

We consider the nonlinear Schrödinger equation with a focusing cubic term and a
defocusing quintic nonlinearity in dimensions two and three. The main interest of this article …

Cette thèse est consacrée à l'étude mathématique de deux systèmes quantiques décrits par
des modèles non linéaires: le polaron anisotrope et les électrons d'un cristal périodique …

We study a 1D nonlinear Schrödinger equation appearing in the description of a particle
inside an atomic nucleus. For various nonlinearities, the ground states are discussed and …

In this thesis, I will describe the different research works that I have carried out since the
defense of my PhD. My PhD thesis [1] was devoted to the mathematical study of two …

We study vacuum polarisation effects of a Dirac field coupled to an external scalar field and
derive a semi-classical expansion of the regularised vacuum energy. The leading order of …