8 citations · 24 across the 11 of their papers we have counts for
11 papers
Qualitative analysis on the critical points of the Robin function
Francesca Gladiali, Massimo Grossi, Peng Luo +1
Let be a smooth bounded domain with and where is the ball centered at and radius . In this paper, we est…
Non-degeneracy and existence of new solutions for the Schrödinger equations
Yuxia Guo, Monica Musso, Shuangjie Peng +1
We consider the following nonlinear problem $$ (P) \quad \quad - Δu + V(|y|)u=u^{p},\quad u>0 \quad \mbox{in} \ {\mathbb{R}}^N, \quad u \in H^1({\mathbb{R}}^N), $$ where is…
Non-degeneracy and local uniqueness of positive solutions to the Lane-Emden problem in dimension two
Massimo Grossi, Isabella Ianni, Peng Luo +1
We are concerned with the Lane-Emden problem \begin{equation*} \begin{cases} -Δu=u^{p} &{\text{in}~Ω},\\[0.5mm] u>0 &{\text{in}~Ω},\\[0.5mm] u=0 &{\text{on}~\partial Ω}, \end{cases…
Local uniqueness of vortices for 2D steady Euler flow in a bounded domain
Daomin Cao, Weilin Yu, Changjun Zou
We study the 2D Euler equation in a bounded simply-connected domain, and establish the local uniqueness of flow whose stream function satisfies \begin{equation*} \b…
Excited states on Bose-Einstein condensates with attractive interactions
Peng Luo, Shuangjie Peng, Shusen Yan
We study the Bose-Einstein condensates (BEC) in two or three dimensions with attractive interactions, described by constraint Gross-Pitaevskii energy functional. First, we…
Infinitely many non-radial solutions to a critical equation on annulus
Yuxia Guo, Benniao Li, Angela Pistoia +1
In this paper, we build infinitely many non-radial sign-changing solutions to the critical problem: \begin{equation*} \left\{\begin{array}{rlll} -Δu&=|u|^{\frac{4}{N-2}}u, &\hbox{…
Uniqueness of planar vortex patch in incompressible steady flow
Daomin Cao, Yuxia Guo, Shuangjie Peng +1
We investigate a steady planar flow of an ideal fluid in a bounded simple connected domain and focus on the vortex patch problem with prescribed vorticity strength. There are two m…
Existence and local uniqueness of bubbling solutions for poly-harmonic equations with critical growth
Yuxia Guo, Shuangjie Peng, Shusen Yan
\begin{abstract} We consider the following poly-harmonic equations with critical exponents: \begin{equation}\label{P} (-Δ)^m u =K(y)u^{\frac{N+2m}{N-2m}},\;\;\; u>0\;\;\;\hbox{in}…
Equations involving fractional Laplacian operator: Compactness and application
Shusen Yan, Jianfu Yang, Xiaohui Yu
In this paper, we consider the following problem involving fractional Laplacian operator: \begin{equation}\label{eq:0.1} (-Δ)^α u= |u|^{2^*_α-2-\varepsilon}u + λu\,\, {\rm in}\,\,…
On the Webster scalar curvature problem on the CR sphere with a cylindrical-type symmetry
Daomin Cao, Shuangjie Peng, Shusen Yan
By variational methods, for a kind of Webster scalar curvature problems on the CR sphere with cylindrically symmetric curvature, we construct some multi-peak solutions as the param…
Infinitely many solution for prescribed curvature problem on
Juncheng Wei, Shusen Yan
We consider the following prescribed scalar curvature problem on (*)$$\left\{\begin{array}{l} - Δ_{S^N} u + \frac{N(N-2)}{2} u = \tilde{K} u^{\frac{N+2}{N-2}} {on} S^N, u >0…