11 papers
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 $$ -\nabla \cdot \left(|x|^{2a} \nabla u\ri…
NLS equation with competing inhomogeneous nonlinearities: ground states, blow-up, and scattering
Tianxiang Gou, Mohamed Majdoub, Tarek Saanouni
We investigate a class of nonlinear equations of Schrödinger type with competing inhomogeneous nonlinearities in the non-radial inter-critical regime, \begin{align*} i \partial_t…
Non-degeneracy and uniqueness of ground states to nonlinear elliptic equations with mixed local and nonlocal operators
Tianxiang Gou
This paper concerns the non-degeneracy and uniqueness of ground states to the following nonlinear elliptic equation with mixed local and nonlocal operators, $$ -Îu +(-Î)^s u + λ…
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 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: $$…
Normalized solutions to nonlinear Schrödinger equations with competing Hartree-type nonlinearities
Divyang Bhimani, Tianxiang Gou, Hichem Hajaiej
In this paper, we consider solutions to the following nonlinear Schrödinger equation with competing Hartree-type nonlinearities, $$ -Îu + λu=\left(|x|^{-γ_1} \ast |u|^2\right)…