26 citations · 174 across the 43 of their papers we have counts for
5 papers · 1 filter
Existence, non-existence and blow-up behavior of minimizers for the mass-critical fractional nonlinear Schrödinger equations with periodic potentials
Van Duong Dinh
We consider the minimizing problem for the energy functional with prescribed mass constraint related to the fractional nonlinear Schrödinger equation with periodic potentials. Usin…
Energy scattering for a class of inhomogeneous nonlinear Schrödinger equation in two dimensions
Van Duong Dinh
We consider a class of -supercritical inhomogeneous nonlinear Schrödinger equations in two dimensions \[ i\partial_t u + Δu = \pm |x|^{-b} |u|^αu, \quad (t,x) \in \mathbb{R} \…
Global dynamics for a class of inhomogeneous nonlinear Schrödinger equations with potential
Van Duong Dinh
We consider a class of -supercritical inhomogeneous nonlinear Schrödinger equations with potential in three dimensions \[ i\partial_t u + Δu - V u = \pm |x|^{-b} |u|^αu, \quad…
Some qualitative studies of the focusing inhomogeneous Gross-Pitaevskii equation
Alex H. Ardila, Van Duong Dinh
We study the Cauchy problem for an inhomogeneous Gross-Pitaevskii equation. We first derive a sharp threshold for global existence and blow up of the solution. Then we construct an…
On nonlinear Schrödinger equations with attractive inverse-power potentials
Van Duong Dinh
We study the Cauchy problem for nonlinear Schrödinger equations with attractive inverse-power potentials. By using variational arguments, we first determine a sharp threshold of gl…