8 papers · 1 filter
Positive normalized solutions to a singular elliptic equation with a -supercritical nonlinearity
Siyu Chen, Xiaojun Chang, Jiazheng Zhou
This paper studies the existence of positive normalized solutions to the singular elliptic equation \[ -Δu + λu = u^{-r} + u^{p-1} \quad \text{in } Ω, \] with the Dirichlet boundar…
Normalized solutions of supercritical NLS equations in exterior domains with inhomogeneous nonlinearities
Xiaojun Chang, Cong-Mei Li
This paper establishes the existence of normalized mountain pass solutions to the -supercritical nonlinear Schrödinger equation with inhomogeneous nonlinearity $|x|^{-α}|u|^{p…
Normalized solutions for a Sobolev critical quasilinear Schrödinger equation
Yuxin Li, Meijie Yang, Xiaojun Chang
In this paper, we study the existence of normalized solutions for the following quasilinear Schrödinger equation with Sobolev critical exponent: \begin{eqnarray*} -Δu-uΔ(u^2)+λu=τ|…
Positive normalized solutions of Schrödinger equations with Sobolev critical growth in bounded domains
Xiaojun Chang, Manting Liu, Duokui Yan
This paper investigates the existence of positive normalized solutions to the Sobolev critical Schrödinger equation: \begin{equation*} \left\{ \begin{aligned} &-Δu +λu =|u|^{2^*-2}…
Standing waves with prescribed mass for NLS equations with Hardy potential in the half-space under Neumman boundary condition
Yuxuan Zhang, Xiaojun Chang, Lin Chen
Consider the Neumann problem: \begin{eqnarray*} \begin{cases} &-Δu-\fracμ{|x|^2}u +λu =|u|^{q-2}u+|u|^{p-2}u ~~~\mbox{in}~~\mathbb{R}_+^N,~N\ge3, &\frac{\partial u}{\partial ν}=0 ~…
Solutions with prescribed mass for -supercritical NLS equations under Neumann boundary conditions
Xiaojun Chang, Vicenţiu D. Rădulescu, Yuxuan Zhang
In this paper, we investigate the following nonlinear Schrödinger equation with Neumann boundary conditions: \begin{equation*} \begin{cases} -Δu+ λu= f(u) & {\rm in} \,~ Ω,\\ \disp…