Uniqueness and nondegeneracy of ground states for (-Δ)^su+u=2(I₂⋆ u²)u in ℝ^N when s is close to 1

2023/03/26 by Luo, Huxiao
#35A02 #35B20 #35J61 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.14610

Abstract

In this article, we study the uniqueness and nondegeneracy of ground states to a fractional Choquard equation of the form: (-Δ)^su+u=2(I₂⋆ u²)u where s∈(0,1) is sufficiently close to 1. Our method is to make a continuation argument with respect to the power s∈(0,1) appearing in (-Δ)^s. This approach is based on [M. M. Fall and E. Valdinoci, Comm. Math. Phys., 329 (2014) 383-404].

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