3 citations · 3 across the 10 of their papers we have counts for
10 papers
Nondegeneracy of bubble solutions to the Choquard equation in two dimension
Jinkai Gao, Xinfu Li, Shiwang Ma
In this paper, we study the following Choquard equation with exponential nonlinearity \begin{equation*} -Δu=\left(\int_{\R^{2}}\frac{e^{u(y)}}{|x-y|^α}dy\right)e^{u(x)},\quad \text…
Asymptotic behavior of the least energy solutions to the Choquard equation in dimension two
Jinkai Gao, Xinfu Li, Shiwang Ma
In this paper, we are interested in the following planar Choquard equation \begin{equation*} \begin{cases} -Δu=\displaystyle\left(\int\limits_Ω\frac{u^{p+1}(y)}{|x-y|^α}dy\right)u^…
Normalized solutions to lower critical Choquard equation in mass-supercritical setting
Shuai Mo, Shiwang Ma
We study the normalized solutions to the following Choquard equation \begin{equation*} \aligned &-Δu + λu =μg(u) + γ(I_α* |u|^{\frac{N+α}{N}})|u|^{\frac{N+α}{N}-2}u & \text{in\ \ }…
Asymptotic behavior of multi-peak solutions to the Brezis-Nirenberg problem. The sub-critical perturbation case
Jinkai Gao, Shiwang Ma
In this paper, we consider the following well-known Brezis-Nirenberg problem \begin{equation*} \begin{cases} -Δu= u^{2^*-1}+\varepsilon u^{q-1}, \quad u>0, &{\text{in}~Ω},\\ \quad…
Asymptotic behavior for the Brezis-Nirenberg problem. The subcritical perturbation case
Jinkai Gao, Shiwang Ma
In this paper, we are concerned with the well-known Brezis-Nirenberg problem \begin{equation*} \begin{cases} -Δu= u^{2^*-1}+\varepsilon u^{q-1},\quad u>0, &{\text{in}~Ω},\\ \quad \…
Existence of positive solutions for Kirchhoff type problems with critical exponent in exterior domains
Liqian Jia, Xinfu Li, Shiwang Ma
In this paper, by using variational methods we study the existence of positive solutions for the following Kirchhoff type problem: $$ \left\{ \begin{array}{ll} -\left(a+b\mathlarge…
Asymptotic profiles for Choquard equations with general critical nonlinearities
Xiaonan Liu, Shiwang Ma, Yachen Wang
In this paper, we study asymptotic behavior of positive ground state solutions for the nonlinear Choquard equation: \begin{equation}\label{0.1} -Δu+\varepsilon u=\big(I_α\ast F(u)\…
Asymptotic profiles of ground state solutions for Choquard equations with a general local perturbation
Shiwang Ma, Vitaly Moroz
In this paper, we study the asymptotic behavior of ground state solutions for the nonlinear Choquard equation with a general local perturbation $$ -Δu+\varepsilon u=(I_α\ast |u|^{p…
Non-existence and multiplicity of positive solutions for Choquard equations with critical combined nonlinearities
Shiwang Ma
We study the non-existence and multiplicity of positive solutions of the nonlinear Choquard type equation $$ -Δu+ \varepsilon u=(I_α\ast |u|^{p})|u|^{p-2}u+ |u|^{q-2}u, \quad {\rm…
Asymptotic profiles for a nonlinear Schrödinger equation with critical combined powers nonlinearity
Shiwang Ma, Vitaly Moroz
We study asymptotic behaviour of positive ground state solutions of the nonlinear Schrödinger equation where $N\ge…