Local uniqueness of semiclassical bounded states for a singularly perturbed fractional Kirchhoff problem

2022/03/14 by Rădulescu, Vicentiu D., Yang, Zhipeng
#35A15 #35R11 #47G20 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2203.07466

Abstract

In this paper, we consider the following singularly perturbed fractional Kirchhoff problem (ε^2sa+ε^4s-N b∫_ℝ^N|(-Δ)^(s)/(2)u|²dx)(-Δ)^su+V(x)u=|u|^p-2u, in ℝ^N, where a,b>0, 2s 0 sufficiently small and a bounded continuous function V, we establish a type of local Pohozǎev identity by extension technique and then we can obtain the local uniqueness of semiclassical bounded solutions based on our recent results on the uniqueness and non-degeneracy of positive solutions to the limit problem.

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