Groundstates for Choquard equations with the upper critical exponent

2018/12/14 by Xinfu Li, Shiwang Ma, Li, Xinfu +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Compact space #Constraint (computer-aided design) #Critical exponent #Exponent #FOS: Mathematics #Geometry #Lemma (botany) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons #Pure mathematics #Scaling #Upper and lower bounds #math.AP

paper · pdf · doi:10.48550/arxiv.1812.05761

published in arXiv (Cornell University) (Cornell University)

arxiv created 2018/12/14 · openalex publication_date 2018/12/14 · arxiv updated 2018/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 compactness lemma of Strauss, a groundstate solution in H¹(ℝ^N) which is positive and radially symmetric is obtained. The result here extends and complements the earlier theorems.

Citations

• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• Groundstates of nonlinear Choquard equations: Existence, qualitative properties and decay asymptotics
• Existence of solitary waves in higher dimensions
• On Gravity's role in Quantum State Reduction

Related

• Normalized solutions to lower critical Choquard equation in mass-supercritical setting
• High energy solution of the Choquard equation
• Groundstates of nonlinear Choquard equations: Existence, qualitative properties and decay asymptotics
• Uniqueness, symmetry and convergence of positive ground state solutions of the Choquard type equation on a ball
• Ground state solutions for a nonlinear Choquard equation