76 citations · 186 across the 13 of their papers we have counts for
13 papers
Qualitative analysis for Moser-Trudinger nonlinearities with a low energy
Peng Luo, Kefan Pan, Shuangjie Peng
We are concerned with the Moser-Trudinger problem \begin{equation*} \begin{cases} -Δu=λue^{u^2}~~&\mbox{in}~Ω,\\[0.5mm] u>0 ~~ &{\text{in}~Ω},\\[0.5mm] u=0~~&\mbox{on}~\partial Ω,…
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…
Concentrated solutions to fractional Schrödinger equations with prescribed -norm
Qing Guo, Peng Luo, Chunhua Wang +1
We investigate the existence and local uniqueness of normalized -peak solutions for the fractional Schrödinger equations with attractive interactions with a class of degenerated…
Existence and local uniqueness of normalized peak solutions for a Schrodinger-Newton system
Qing Guo, Peng Luo, Chunhua Wang +1
In this paper, we investigate the existence and local uniqueness of normalized peak solutions for a Schrödinger-Newton system under the assumption that the trapping potential is de…
On the number and location of critical points of solutions of nonlinear elliptic equations in domains with a small hole
Massimo Grossi, Peng Luo
In this paper we study the following problem \begin{equation} \begin{cases} -Δu=f(u)~&\mbox{in}\ Ω_\varepsilon,\\ u>0~&\mbox{in}\ Ω_\varepsilon,\\ u=0~&\mbox{on}\ \partialΩ_\vareps…
The number of positive solutions to the Brezis-Nirenberg problem
Daomin Cao, Peng Luo, Shuangjie Peng
In this paper we are concerned with the well-known Brezis-Nirenberg problem \begin{equation*} \begin{cases} -Δu= u^{\frac{N+2}{N-2}}+\varepsilon u, &{\text{in}~Ω},\\ u>0, &{\text{i…
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…
Positive multi-peak solutions for a logarithmic Schrodinger equation
Peng Luo, Yahui Niu
In this manuscript, we consider the logarithmic Schrödinger equation \begin{eqnarray*} -\varepsilon^2Δu+V(x)u=u\log u^{2},\,\,\,u>0, & \text{in}\,\,\,\mathbb{R}^{N}, \end{eqnarray*…
Multi-peak positive solutions to a class of Kirchhoff equations
Peng Luo, Shuangjie Peng, Chunhua Wang +1
In the present paper, we consider the nonlocal Kirchhoff problem \begin{eqnarray*} -\left(ε^2a+εb\int_{\mathbb{R}^{3}}|\nabla u|^{2}\right)Δu+V(x)u=u^{p},\,\,\,u>0 & & \text{in }\m…
Uniqueness and Nondegeneracy of positive solutions to Kirchhoff equations and its applications in singular perturbation problems
Gongbao Li, Peng Luo, Shuangjie Peng +2
In the present paper, we establish the uniqueness and nondegeneracy of positive energy solutions to the Kirchhoff equation \begin{eqnarray*} -\left(a+b\int_{\mathbb{R}^{3}}|\nabla…
Uniqueness of positive solutions with Concentration for the Schrödinger-Newton problem
Peng Luo, Shuangjie Peng, Chunhua Wang
We are concerned with the following Schrödinger-Newton problem \begin{equation} -\varepsilon^2Δu+V(x)u=\frac{1}{8π\varepsilon^2} \big(\int_{\mathbb R^3}\frac{u^2(ξ)}{|x-ξ|}dξ\big)u…
Uniqueness and nondegeneracy of positive solutions to a class of Kirchhoff equations in
Gongbao Li, Shuangjie Peng, Chang-Lin Xiang
In this paper, we establish a type of uniqueness and nondegeneracy results for positive solutions to the following nonlocal Kirchhoff equations \begin{eqnarray*} -\left(a+b\int_{\m…
Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations
Daomin Cao, Shuanglong Li, Peng Luo
We are concerned with the following nonlinear Schrödinger equation where , . For …