We survey old and recent results dealing with the existence and properties of solutions to
the Choquard type equations-Δ u+ V (x) u=\left (| x|^-(N-α)*| u|^ p\right)| u|^ p-2 u\quad …

We consider a semilinear elliptic problem where Iα is a Riesz potential and p> 1. This family
of equations includes the Choquard or nonlinear Schrödinger–Newton equation. For an …

We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear
Choquard equation $$-\Delta u=\left (\int_ {\Omega}\frac {| u|^{2_ {\mu}^{\ast}}}{| xy|^{\mu}} …

In this paper we study the semiclassical limit for the singularly perturbed Choquard
equation− ε 2 Δ u+ V (x) u= ε μ− 3 (∫ R 3 Q (y) G (u (y))| x− y| μ dy) Q (x) g (u) in R 3, where …

We study the nonlocal equation-ε^ 2 Δ u_ ε+ V u_ ε= ε^-α\bigl (I_ α*| u_ ε|^ p\bigr)| u_ ε|^ p-2
u_ ε\quad in R^ N,-ε 2 Δ u ε+ V u ε= ε-α (I α∗| u ε| p)| u ε| p-2 u ε in RN, where N ≥ 1 N≥ 1, α …

The aim of this book is to collect a set of results concerning nonlinear Schrödinger equations
in the whole space driven by fractional operators. The material presented here was mainly …

We study the following singularly perturbed nonlocal Schrödinger equation− ε 2 Δ u+ V (x)
u= ε μ− 2 [1| x| μ⁎ F (u)] f (u) in R 2, where V (x) is a continuous real function on R 2, F (s) is …

We consider the general Choquard equations− Δ u+ u=(I α⁎| u| p)| u| p− 2 u where I α is a
Riesz potential. We construct minimal action odd solutions for p∈(N+ α N, N+ α N− 2) and …

We prove existence of infinitely many solutions u∈ H r 1 (RN) for the nonlinear Choquard
equation-Δ u+ μ u=(I α∗ F (u)) f (u) in RN, where N≥ 3, α∈(0, N), I α (x):= Γ (N-α 2) Γ (α 2) π …

We consider the following nonlinear Choquard equation with Dirichlet boundary condition−
Δ u=(∫ Ω| u| 2 μ⁎| x− y| μ dy)| u| 2 μ⁎− 2 u+ λ f (u) in Ω, where Ω is a smooth bounded …