Limit profiles and uniqueness of ground states to the nonlinear Choquard equations

2017/04/01 by Jinmyoung Seok, Seok, Jinmyoung
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1704.00126

18 pages, revised version

openalex publication_date 2017/04/01 · arxiv created 2018/02/06 · arxiv updated 2018/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider nonlinear Choquard equations \-Δu +u · = · (I_α*|u|^p)|u|^p-2u in ℝ^N,
lim_{x → ∞}u(x) · = · 0,. where I_α denotes Riesz potential and α∈ (0, N). In this paper, we investigate limit profiles of ground states of nonlinear Choquard equations as α→ 0 or α→ N. This leads to the uniqueness and nondegeneracy of ground states when α is sufficiently close to 0 or close to N.

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

Related

• Existence and nonexistence of solutions to Choquard equations
• Asymptotic profiles for Choquard equations with general critical nonlinearities
• Asymptotic profiles of ground state solutions for Choquard equations with a general local perturbation
• Uniqueness and Nondegeneracy of Ground States for Choquard Equations in three dimensions
• Ground state solutions for a nonlinear Choquard equation