81 citations · 93 across the 20 of their papers we have counts for
20 papers
Non-degeneracy and uniqueness of ground states to nonlinear elliptic equations with mixed local and nonlocal operators
Tianxiang Gou
This paper concerns the non-degeneracy and uniqueness of ground states to the following nonlinear elliptic equation with mixed local and nonlocal operators, $$ -Δu +(-Δ)^s u + λu=|…
Fractional Morrey-Sobolev type embeddings and nonlocal subelliptic problems with oscillating nonlinearities on stratified Lie groups
Sekhar Ghosh, Tianxiang Gou, Vishvesh Kumar +1
In this paper, we establish the fractional Morrey-Sobolev type embeddings on stratified Lie groups. This extends and complements the Sobolev type embeddings derived in \cite{GKR}.…
Radial symmetry, uniqueness and non-degeneracy of solutions to degenerate nonlinear Schrödinger equations
Tianxiang Gou
In this paper, we consider the radial symmetry, uniqueness and non-degeneracy of solutions to the degenerate nonlinear elliptic equation $$ -\nabla \cdot \left(|x|^{2a} \nabla u\ri…
Radial 3D Focusing Energy Critical INLS equations with defocusing perturbation: Ground states, Scattering, and Blow-up
Tianxiang Gou, Mohamed Majdoub, Tarek Saanouni
We investigate the following inhomogeneous nonlinear Schrödinger equation in the radial regime, featuring a focusing energy-critical nonlinearity and a defocusing perturbation: $$…
Uniqueness of positive solutions to fractional nonlinear elliptic equations with harmonic potential
Tianxiang Gou, Vicentiu D. Radulescu
In this paper, we establish the uniqueness of positive solutions to the following fractional nonlinear elliptic equation with harmonic potential \begin{align*} (-Δ)^s u+ \left(ω+|x…
Blow-up of cylindrically symmetric solutions for Fractional NLS
Tianxiang Gou, Vicentiu D. Radulescu, Zhitao Zhang
In this paper, we consider blow-up of solutions to the Cauchy problem for the following fractional NLS, $$ \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 , $$ \left\{ \begin{aligned} &\textnormal{i}\partia…
NLS equation with competing inhomogeneous nonlinearities: ground states, blow-up, and scattering
Tianxiang Gou, Mohamed Majdoub, Tarek Saanouni
We investigate a class of nonlinear equations of Schrödinger type with competing inhomogeneous nonlinearities in the non-radial inter-critical regime, \begin{align*} i \partial_t u…
Standing waves with prescribed -norm to nonlinear Schrödinger equations with combined inhomogeneous nonlinearities
Tianxiang Gou
In this paper, we are concerned with solutions to the following nonlinear Schrödinger equation with combined inhomogeneous nonlinearities, $$ -Δu + λu= μ|x|^{-b}|u|^{q-2} u + |x|^{…
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{…
Non-autonomous double phase eigenvalue problems with indefinite weight and lack of compactness
Tianxiang Gou, Vicentiu D. Radulescu
In this paper, we consider eigenvalues to the following double phase problem with unbalanced growth and indefinite weight, $$ -Δ_p^a u-Δ_q u =λm(x) |u|^{q-2}u \quad \mbox{in} \,\,…
Existence and dynamics of normalized solutions to nonlinear Schrödinger equations with mixed fractional Laplacians
Lassaad Chergui, Tianxiang Gou, Hichem Hajaiej
In this paper, we are concerned with the existence and dynamics of solutions to the equation with mixed fractional Laplacians unde…
Normalized solutions to nonlinear Schrödinger equations with competing Hartree-type nonlinearities
Divyang Bhimani, Tianxiang Gou, Hichem Hajaiej
In this paper, we consider solutions to the following nonlinear Schrödinger equation with competing Hartree-type nonlinearities, $$ -Δu + λu=\left(|x|^{-γ_1} \ast |u|^2\right) u -…
Uniqueness of ground states to fractional nonlinear elliptic equations with harmonic potential
Tianxiang Gou
In this paper, we prove the uniqueness of ground states to the following fractional nonlinear elliptic equation with harmonic potential, $$ (-Δ)^s u+ \left(ω+|x|^2\right) u=|u|^{p-…
Orbital stability and concentration of standing waves to nonlinear Schrödinger systems with mass critical exponent
Daniele Garrisi, Tianxiang Gou
For a nonlinear Schrödinger system with mass critical exponent, we prove the existence and orbital stability of standing-wave solutions obtained as minimizers of the underlying ene…
Blowup of cylindrically symmetric solutions for biharmonic NLS
Tianxiang Gou
In this paper, we consider blowup of solutions to the Cauchy problem for the following biharmonic nonlinear Schrödinger equation (NLS), $$ \textnormal{i} \, \partial_t u=Δ^2 u-μΔu-…
Higher topological type semiclassical states for fractional nonlinear elliptic equations
Shaowei Chen, Tianxiang Gou
In this paper, we are concerned with semiclassical states to the following fractional nonlinear elliptic equation, \begin{align*} \eps^{2s}(-Δ)^s u + V(x) u=\mathcal{N}(|u|)u \quad…
Higher topological type semiclassical states for Sobolev critical Dirac equations with degenerate potential
Shaowei Chen, Tianxiang Gou
In this paper, we are concerned with semiclassical states to the following Sobolev critical Dirac equation with degenerate potential, \begin{align*} -\textnormal{i} \eps α\cdot \na…
Normalized solutions to the mixed dispersion nonlinear Schrödinger equation in the mass critical and supercritical regime
Denis Bonheure, Jean-Baptiste Casteras, Tianxiang Gou +1
In this paper, we study the existence of solutions to the mixed dispersion nonlinear Schrödinger equation under the constr…
Existence and orbital stability of standing waves for nonlinear Schrödinger systems
Tianxiang Gou, Louis Jeanjean
In this paper we investigate the existence of solutions in for nonlinear Schrödinger systems of the form \[ \left\{ \begin{aligned} -Δu_1 &= λ_1 u_1 + μ_…