在$\mathbb{R}^n$, $n\ge 3$中$Δu-u+|u|^{p-1}u= 0$的约束状态的唯一性

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-10 DOI:arxiv-2409.06915

Moxun Tang

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摘要

我们对 Berestycki 和 Lions 于 1983 年提出的关于 $\mathbb{R}^n$, $u\inH^1(\mathbb{R}^n)$, $u\not\equiv 0$, $n\ge 3$ 中 $\Delta u +f(u)=0$ 约束态唯一性的猜想给出了肯定的答案。对于模型非线性$f(u)=-u+|u|^{p-1}u$，$10$。

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Uniqueness of bound states to $Δu-u+|u|^{p-1}u= 0$ in $\mathbb{R}^n$, $n\ge 3$

We give a positive answer to a conjecture of Berestycki and Lions in 1983 on the uniqueness of bound states to $\Delta u +f(u)=0$ in $\mathbb{R}^n$, $u\in H^1(\mathbb{R}^n)$, $u\not\equiv 0$, $n\ge 3$. For the model nonlinearity $f(u)=-u+|u|^{p-1}u$, $10$.

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arXiv - MATH - Analysis of PDEs

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