5 papers
Semiclassical solutions for critical Schrödinger-Poisson systems involving multiple competing potentials
Lingzheng Kong, Haibo Chen
In this paper, a class of Schrödinger-Poisson system involving multiple competing potentials and critical Sobolev exponent is considered. Such a problem cannot be studied with the…
Existence and multiplicity of positive solutions for fractional Laplacian systems with nonlinear coupling
Guofeng Che, Haibo Chen, Tsung-fang Wu
It is well known that a single nonlinear fractional Schrödinger equation with a potential and a small parameter may have a positive solution that is concentra…
The minimizing problem involving p--Laplacian and Hardy--Littlewood--Sobolev upper critical exponent
Yu Su, Haibo Chen
In this paper, we study the minimizing problem: $$ S_{p,1,α,μ}:= \inf_{u\in W^{1,p}(\mathbb{R}^{N})\setminus\{0\}} \frac{ \int_{\mathbb{R}^{N}}|\nabla u|^{p}\mathrm{d}x - μ\int_{\m…
Elliptic problem involving finite many critical exponents in
Yu Su, Haibo Chen
In this paper, we consider the following problem $$ -Δu -ζ\frac{u}{|x|^{2}} = \sum_{i=1}^{k} \left( \int_{\mathbb{R}^{N}} \frac{|u|^{2^{*}_{α_{i}}}}{|x-y|^{α_{i}}} \mathrm{d}y \rig…
Fractional Elliptic problem with Finite many critical Hardy--Sobolev Exponents
Yu Su, Haibo Chen
In this paper, we consider the following problem: $$ (-Δ)^{s} u -\frac{ζu}{|x|^{2s}} = \sum_{i=1}^{k} \frac{|u|^{2^{*}_{s,θ_{i}}-2}u} {|x|^{θ_{i}}} , \mathrm{~in~} \mathbb{R}^{N},…