68 citations · 75 across the 13 of their papers we have counts for
13 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^…
Existence of normalized solutions to Choquard equation with general mixed nonlinearities
Meiling Zhu, Xinfu Li
We study the existence of normalized solutions to the following Choquard equation with being a Berestycki-Lions type function \begin{equation*} \begin{cases} -Δu+λu=(I_α\ast F(…
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…
Normalized solutions to lower critical Choquard equation with a local perturbation
Xinfu Li, Jianguang Bao, Wenguang Tang
In this paper, we study the existence and non-existence of normalized solutions to the lower critical Choquard equation with a local perturbation \begin{equation*} \begin{cases} -Δ…
Multiplicity and orbital stability of normalized solutions to non-autonomous Schrödinger equation with mixed nonlinearities
Xinfu Li, Li Xu, Meiling Zhu
This paper studies the multiplicity of normalized solutions to the Schrödinger equation with mixed nonlinearities \begin{equation*} \begin{cases} -Δu=λu+h(εx)|u|^{q-2}u+η|u|^{p-2}u…
Studies of normalized solutions to Schrödinger equations with Sobolev critical exponent and combined nonlinearities
Xinfu Li
We consider the Sobolev critical Schrödinger equation with combined nonlinearities \begin{equation*} \begin{cases} -Δu=λu+|u|^{2^*-2}u+μ|u|^{q-2}u,\ \ x\in\mathbb{R}^{N},\\ u\in H^…
Standing waves to upper critical Choquard equation with a local perturbation: multiplicity, qualitative properties and stability
Xinfu Li
In this paper, we consider the upper critical Choquard equation with a local perturbation \begin{equation*} \begin{cases} -Δu=λu+(I_α\ast|u|^{p})|u|^{p-2}u+μ|u|^{q-2}u,\ x\in \math…
Nonexistence, existence and symmetry of normalized ground states to Choquard equations with a local perturbation
Xinfu Li
We study the Choquard equation with a local perturbation \begin{equation*} -Δu=λu+(I_α\ast|u|^p)|u|^{p-2}u+μ|u|^{q-2}u,\ x\in \mathbb{R}^{N} \end{equation*} having prescribed mass…
Global existence and blowup for Choquard equations with an inverse-square potential
Xinfu Li
In this paper, the Choquard equation with an inverse-square potential and both focusing and defocusing nonlinearities in the energy-subcritical regime is investigated. For all the…
Groundstates for Choquard equations with the upper critical exponent
Xinfu Li, Shiwang Ma
In this paper, an autonomous Choquard equation with the upper critical exponent is considered. By using the Pohožaev constraint method, the subcritical approximation method and the…
Orbital stability of standing waves for Schrödinger type equations with slowly decaying linear potential
Xinfu Li, Junying Zhao
In this paper, kinds of Schrödinger type equations with slowly decaying linear potential and power type or convolution type nonlinearities are considered. By using the concentratio…
Choquard equations with critical nonlinearities
Xinfu Li, Shiwang Ma
In this paper, we study the Brezis-Nirenberg type problem for Choquard equations in \begin{equation*} -Δu+u=(I_α\ast|u|^{p})|u|^{p-2}u+λ|u|^{q-2}u \quad \mathrm{in}\…