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

Moxun Tang

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arXiv · 2409.06915

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

Moxun Tang

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Abstract

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 $f(u)=-u+|u|^{p-1}u$, $1 0$.

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Moxun Tang. 2024-09-10. Uniqueness of bound states to $\Delta u-u+|u|^{p-1}u= 0$ in $\mathbb{R}^n$, $n\ge 3$. https://arxiv.org/abs/2409.06915

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