1 citations · 3 across the 12 of their papers we have counts for
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On the Number of Normalized Ground State Solutions for a class of Elliptic Equations with general nonlinearities and potentials
Hichem Hajaiej, Eliot Pacherie, Linjie Song
We provide a precise description of the set of normalized ground state solutions (NGSS) for the class of elliptic equations: $$ -Δu - λu + V (| x |) u - f (| x |, u) = 0,\quad\text…
On the focusing fractional nonlinear Schrödinger equation on the waveguide manifolds
Amin Esfahani, Hichem Hajaiej, Yongming Luo +1
In this paper, we consider the focusing fractional nonlinear Schrödinger equation (FNLS) on the waveguide manifolds both in the isotropic and aniso…
On radial positive normalized solutions of the Nonlinear Schrödinger equation in an annulus
Jian Liang, Linjie Song
We are interested in the following semilinear elliptic problem: \begin{equation*} \begin{cases} -Δu + λu = u^{p-1} \ \text{in} \ T,\\ u > 0, u = 0 \ \text{on} \ \partial T,\\ \int_…
Existence and instability of standing waves for the biharmonic nonlinear Schroedinger equation with combined nonlinearities
Xiaojun Chang, Hichem Hajaiej, Zhouji Ma +1
We prove the existence of normalized ground state solutions for the biharmonic Schrödinger equation with combined nonlinearities and show that all ground states correspond to the l…
Positive solution for an elliptic system with critical exponent and logarithmic terms
Hichem Hajaiej, Tianhao Liu, Linjie Song +1
In this paper, we study the existence and nonexistence of positive solutions for a coupled elliptic system with critical exponent and logarithmic terms. The presence of the the log…
On the Eigenvalues of the Fractional Laplacian
Sabri Bahrouni, Hichem Hajaiej, Linjie Song
We consider the eigenvalue problem for the fractional Laplacian \begin{equation} \left\{\begin{aligned} (- Δ)_p^{s}\, u + μ(- Δ)_q^{s}\, u+ |u|^{p-2}u+μ|u|^{q-2}u=λ V(x)|u…
Uniqueness of normalized ground states for NLS models
Hichem Hajaiej, Linjie Song
We present two methods to prove the uniqueness of normalized ground states. We will first discuss the key ideas and ingredients of each method. Then, we will apply them to various…
On existence and stability results for normalized ground states of mass-subcritical biharmonic NLS on
Hichem Hajaiej, Yongming Luo, Linjie Song
We study the focusing mass-subcritical biharmonic nonlinear Schrödinger equation (BNLS) on the product space . Following the crucial scaling arg…
A New Method to prove the Existence, Non-existence, Multiplicity, Uniqueness, and Orbital Stability/Instability of standing waves for NLS with partial confinement
Linjie Song, Hichem Hajaiej
We give a new method to prove the existence, non-existence, multiplicity, orbital stability/instability of standing waves for NLS with partial confinement without the subcritical h…
Threshold for Existence, Non-existence and Multiplicity of positive solutions with prescribed mass for an NLS with a pure power nonlinearity in the exterior of a ball
Linjie Song, Hichem Hajaiej
We obtain threshold results for the existence, non-existence and multiplicity of normalized solutions for semi-linear elliptic equations in the exterior of a ball. To the best of o…
Comment on the Uniqueness of the Ground State Solutions of a Fractional NLS with a Harmonic Potential
H. Hajaiej, L. Song
The uniqueness of the positive ground state solutions of fractional Shrodinger equations with a harmonic potential has not been covered by the breakthrough method developed in [1,…
A General and Unified Method to prove the Uniqueness of Ground State Solutions and the Existence/Non-existence, and Multiplicity of Normalized Solutions with applications to various NLS
Hichem Hajaiej, Linjie Song
We first give an abstract framework to show the uniqueness of Ground State Solutions (GSS) for a large class of PDEs. To the best of our knowledge, all the existing results in the…