Jean Van Schaftingen

Semi-classical states for the Choquard equation

We study the nonlocal equation

Semiclassical stationary states for nonlinear Schrodinger equations with fast decaying potentials

\begin{aligned} -\varepsilon ^2 \Delta u_\varepsilon +V u_\varepsilon = \varepsilon ^{-\alpha }\bigl (I_\alpha *|u_\varepsilon |^p\bigr ) |u_\varepsilon |^{p - 2} u_\varepsilon \quad \text {in }{\mathbb {R}}^N, \end{aligned}

SYMMETRIZATION AND MINIMAX PRINCIPLES

-ε2Δuε+Vuε=ε-α(Iα∗|uε|p)|uε|p-2uεinRN,where

Nodal solutions for the Choquard equation

N \ge 1

Symmetry of solutions of semilinear elliptic problems

N≥1,