4 papers
Uniqueness of positive solutions to fractional nonlinear elliptic equations with harmonic potential
Tianxiang Gou, Vicentiu D. Radulescu
In this paper, we establish the uniqueness of positive solutions to the following fractional nonlinear elliptic equation with harmonic potential \begin{align*} (-Δ)^s u+ \left(ω+|x…
Blow-up of cylindrically symmetric solutions for Fractional NLS
Tianxiang Gou, Vicentiu D. Radulescu, Zhitao Zhang
In this paper, we consider blow-up of solutions to the Cauchy problem for the following fractional NLS, $$ \textnormal{i} \, \partial_t u=(-Δ)^s u-|u|^{2 σ} u \quad \text{in} \,\,…
Solutions for fourth order anisotropic nonlinear Schrödinger equations in
Vladimir Georgiev, Tianxiang Gou
In this paper, we consider solutions to the following fourth order anisotropic nonlinear Schrödinger equation in , $$ \left\{ \begin{aligned} &\textnormal{i}\partia…
On the solitary waves for anisotropic nonlinear Schrödinger models on the plane
Tianxiang Gou, Hichem Hajaiej, Atanas G. Stefanov
The focussing anisotropic nonlinear Schrödinger equation \begin{align*} \mathrm{i} u_t-\partial_{xx} u + (-\partial_{yy})^s u=|u|^{p-2}u \quad \mbox{in}\ \mathbb{R} \times \mathbb{…