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 look for solutions to the Schrödinger-Poisson-Slater equation (0.1)− Δ u+ λ u− γ (| x|− 1⁎|
u| 2) u− a| u| p− 2 u= 0 in R 3, which satisfy‖ u‖ L 2 (R 3) 2= c for some prescribed c> 0 …

In this paper, we study the existence of solutions to the mixed dispersion nonlinear
Schrödinger equation\[\gamma\Delta^ 2 u-\Delta u+\alpha u=| u|^{2\sigma} u,\qquad u\in H …

We study the nonlocal Schrödinger–Poisson–Slater type equation-Δ u+(I_ α* | u |^ p) | u |^ p-
2 u= | u |^ q-2 u\quad in\quad R^ N,-Δ u+(I α∗| u| p)| u| p-2 u=| u| q-2 u in RN, where N ∈ …

We study the mixed dispersion fourth order nonlinear Schrödinger equation i\partial_tψ-
γΔ^2ψ+βΔψ+|ψ|^2σψ=0\textin\mathbbR*R^N, where γ,σ>0 and β∈R. We focus on standing …

In this paper, we study normalized solutions to the Chern-Simons-Schrödinger system,
which is a gauge-covariant nonlinear Schrödinger system with a long-range electromagnetic …

In this paper, we study constraint minimizers u of the planar Schrödinger-Poisson system
with a logarithmic convolution potential ln⁡| x|⁎ u 2 and a logarithmic external potential V …

We prove scaling invariant Gagliardo–Nirenberg type inequalities of the form\begin
{equation*}\|\varphi\| _ {L^ p (\mathbb {R}^ d)}\le C\|\varphi\| _ {\dot H^{s}(\mathbb {R} …

In this paper, we are concerned with the existence and dynamics of solutions to the equation
with mixed fractional Laplacians (-Δ) s 1 u+(-Δ) s 2 u+ λ u=| u| p-2 u under the constraint∫ …

Let $\gamma> 0\, $, $\beta> 0\, $, $\alpha> 0$ and $0<\sigma N< 4$. In the present paper,
we study, for $ c> 0$ given, the constrained minimization problem\begin {equation*}\label …