8 citations · 13 across the 7 of their papers we have counts for
7 papers
Minimal mass blow-up solutions for nonlinear Schrödinger equations with a Hartree nonlinearity
Naoki Matsui
We consider the following nonlinear Schrödinger equation with a Hartree nonlinearity: \[ i\frac{\partial u}{\partial t}+Δu+|u|^{\frac{4}{N}}u\pm\left(\frac{1}{|x|^{2σ}}\star|u|^2\r…
Minimal mass blow-up solutions for nonlinear Schrödinger equations with a singular potential
Naoki Matsui
We consider the following nonlinear Schrödinger equation with an inverse potential: \[ i\frac{\partial u}{\partial t}+Δu+|u|^{\frac{4}{N}}u\pm\frac{1}{|x|^{2σ}}\log|x|u=0 \] in $\m…
Minimal mass blow-up solutions for double power nonlinear Schrödinger equations with an inverse power potential
Naoki Matsui
We consider the following nonlinear Schrödinger equation with double power nonlinearities and an inverse power potential: \[ i\frac{\partial u}{\partial t}+Δu+|u|^{\frac{4}{N}}u+C_…
Minimal-mass blow-up solutions for inhomogeneous nonlinear Schrödinger equations with growth potentials
Naoki Matsui
In this paper, we consider the following equation: \[ i\frac{\partial u}{\partial t}+Δu+g(x)|u|^{\frac{4}{N}}u-Wu=0. \] We construct a critical-mass solution that blows up at a fin…
Remarks on minimal mass blow up solutions for a double power nonlinear Schrödinger equation
Naoki Matsui
We consider the following nonlinear Schrödinger equation with double power nonlinearity \[ i\frac{\partial u}{\partial t}+Δu+|u|^{\frac{4}{N}}u+|u|^{p-1}u=0,\quad 1<p<1+\frac{4}{N}…
Minimal mass blow-up solutions for nonlinear Schrödinger equations with an inverse potential
Naoki Matsui
We consider the following nonlinear Schrödinger equation with an inverse potential: \[ i\frac{\partial u}{\partial t}+Δu+|u|^{\frac{4}{N}}u\pm\frac{1}{|x|^{2σ}}u=0 \] in $\mathbb{R…
Minimal mass blow-up solutions for nonlinear Schrödinger equations with a potential
Naoki Matsui
We consider a mass critical nonlinear Schrödinger equation with a real-valued potential. In this work, we construct a minimal mass solution that blows up at finite time, under weak…