10 citations · 30 across the 10 of their papers we have counts for
10 papers
Ground states of a nonlocal variational problem and Thomas-Fermi limit for the Choquard equation
Damiano Greco, Yanghong Huang, Zeng Liu +1
We study nonnegative optimizers of a Gagliardo-Nirenberg type inequality $$\iint_{\mathbb{R}^N \times \mathbb{R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-α}} dx\, dy\le C\Big(\int_{…
Asymptotic profile of ground states for the Schrödinger-Poisson-Slater equation
Zeng Liu, Vitaly Moroz
We study the Schrödinger-Poisson-Slater equation where and . By using direct variational analy…
Limit profiles for singularly perturbed Choquard equations with local repulsion
Zeng Liu, Vitaly Moroz
We study Choquard type equation of the form where , …
Nonlinear Inequalities with Double Riesz Potentials
Marius Ghergu, Zeng Liu, Yasuhito Miyamoto +1
We investigate the nonnegative solutions to the nonlinear integral inequality a.e. in , where , and…
On a critical Kirchhoff problem in high dimensions
Yisheng Huang, Zeng Liu, Yuanze Wu
In this paper, we consider the following Kirchhoff problem $$ \left\{\aligned -\bigg(a+b\int_Ω|\nabla u|^2dx\bigg)Δu&= λu^{q-1} + μu^{2^*-1}, &\quad \text{in }Ω, \\ u&>0,&\quad\tex…
Positive solutions to an elliptic equation in of the Kirchhoff type
Yisheng Huang, Zeng Liu, Yuanze Wu
In this paper, we consider the following Kirchhoff type problem $$\left\{\aligned&-\biggl(a + b\int_{\mathbb{R}^N} |\nabla u|^2 dx \biggr) Δu + V(x) u = |u|^{p-2}u &\text{ in } \ma…
On finding solutions of a Kirchhoff type problem
Yisheng Huang, Zeng Liu, Yuanze Wu
Consider the following Kirchhoff type problem $$ \left\{\aligned -\bigg(a+b\int_{\mathbb{B}_R}|\nabla u|^2dx\bigg)Δu&= λu^{q-1} + μu^{p-1}, &\quad \text{in}\mathbb{B}_R, \\ u&>0,&\…
On Kirchhoff type equations with critical Sobolev exponent and Naimen's open problems
Yisheng Huang, Zeng Liu, Yuanze Wu
We study the following Brezis-Nirenberg problem of Kirchhoff type $$ \left\{\aligned &-(a+b\int_Ω|\nabla u|^2dx)Δu = λ|u|^{q-2}u + δ|u|^{2}u, &\quad \text{in}\ Ω, \\ &u=0,& \text{o…
On a Kirchhoff type problems with potential well and indefinite potential
Yuanze Wu, Yisheng Huang, Zeng Liu
In this paper, we study the following Kirchhoff type problem:% $$ \left\{\aligned&-\bigg(α\int_{\bbr^3}|\nabla u|^2dx+1\bigg)Δu+(λa(x)+a_0)u=|u|^{p-2}u&\text{ in }\bbr^3,\\% &u\in\…
On a biharmonic equations with steep potential well and indefinite potential
Yisheng Huang, Zeng Liu, Yuanze Wu
In this paper, we study the following biharmonic equations:% $$ \left\{\aligned&Δ^2u-a_0Δu+(λb(x)+b_0)u=f(u)&\text{ in }\bbr^N,\\% &u\in\h,\endaligned\right.\eqno{(\mathcal{P}_λ)}%…