1 citations · 4 across the 18 of their papers we have counts for
19 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} \,\,…