On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents

2016/05/17 by Fashun Gao, Gao, Fashun, Minbo Yang +1 · 4 citations
Mathematics · #35J25 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1605.05038

openalex publication_date 2016/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the following nonlinear Choquard equation with Dirichlet boundary condition -Δu =(∫_Ω\frac|u|^2_μ^∗|x-y|^μdy)|u|^2_μ^∗-2u+λf(u)\hspace4.14mmin\hspace1.14mm Ω, where Ω is a smooth bounded domain of ℝ^N, λ>0, N≥3, 0

Cited by

• On nonlinear elliptic problems with Hardy-Littlewood-Sobolev critical exponent and Sobolev-Hardy critical exponent
• Nonlocal problems with Hardy-Littlewood-Sobolev critical exponent and Hardy potential
• Normalized solutions to a Choquard equation involving mixed local and nonlocal operators
• p-biharmonic Kirchhoff equations with critical Choquard nonlinearity

Related

• Nonlocal Choquard equations involving critical Hardy-Littlewood-Sobolev exponent: the effect of the topology of the domain
• On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation
• Nonlocal problems with Hardy-Littlewood-Sobolev critical exponent and Hardy potential
• Critical exponent Neumann problem with Hardy-Littlewood-Sobolev nonlinearity
• A strongly indefinite Choquard equation with critical exponent due to the Hardy-Littlewood-Sobolev inequality