Xiaomeng Huang

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math.AP2025

Normalized vector solutions of nonlinear SchrÃ¶dinger systems

Xiaomeng Huang, Angela Pistoia, Christophe Troestler +1

Given $I^¼ > 0$ we look for solutions $I^» \in R$ and $v_{1}, \dots, v_{k} \in H^{1} (R^{N})$ of the system \[ \begin{cases} \displaystyle -Îv_i+ Î»v_i+V_i(x)v_i = \sum_{\substac…

math.AP2024

Bubble solution for the critical Hartree equation in pierced domain

Marco Ghimenti, Xiaomeng Huang, Angela Pistoia

In this article, we establish the existence of solutions to the following critical Hartree equation \begin{align*} \begin{cases} -Îu=\left(\int_{Î©_\varepsilon}\frac{u^{2_Î¼^*}}{|…