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arXiv · 2203.07464

A singularly perturbed fractional Kirchhoff problem

Vicentiu D. Rădulescu·Zhipeng Yang
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Abstract

In this paper, we first establish the uniqueness and non-degeneracy of positive solutions to the fractional Kirchhoff problem \begin{equation*} \Big(a+b{\int_{\mathbb{R}^{N}}}|(-\Delta)^{\frac{s}{2}}u|^2dx\Big)(-\Delta)^su+mu=|u|^{p-2}u,\quad \text{in}\ \mathbb{R}^{N}, \end{equation*} where $a,b,m>0$, $0<\frac{N}{4} 0$ sufficiently small and a potential function $V$.

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Vicentiu D. Rădulescu, Zhipeng Yang. 2022-03-14. A singularly perturbed fractional Kirchhoff problem. https://arxiv.org/abs/2203.07464

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