Uniqueness of ground states to fractional nonlinear elliptic equations with harmonic potential

2022/08/25 by Tianxiang Gou, Gou, Tianxiang
Computer Science · Mathematics · #35A02 #35R11 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2208.12068

openalex publication_date 2022/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove the uniqueness of ground states to the following fractional nonlinear elliptic equation with harmonic potential, (-Δ)^s u+ (ω+|x|²) u=|u|^p-2u in \Rⁿ, where n ≥ 1, 0-λ_1,s, 20 is the lowest eigenvalue of (-Δ)^s + |x|². The fractional Laplacian (-Δ)^s is characterized as F((-Δ)^su)(ξ)=|ξ|^2s F(u)(ξ) for ξ∈ \Rⁿ, where F denotes the Fourier transform. This solves an open question in \citeSS concerning the uniqueness of ground states.

Related

• Uniqueness of positive solutions to fractional nonlinear elliptic equations with harmonic potential
• Non-degeneracy and uniqueness of ground states to nonlinear elliptic equations with mixed local and nonlocal operators
• Comment on the Uniqueness of the Ground State Solutions of a Fractional NLS with a Harmonic Potential
• Uniqueness of Positive Solutions for Fractional Schrödinger Equations with General Nonlinearities
• Ground state solution of fractional Schrödinger equations with a general nonlinearity