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arXiv · 1504.06144

Uniqueness of positive bound states with multi-bump for nonlinear Schr\"odinger equations

Daomin Cao·Shuanglong Li·Peng Luo
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Abstract

We are concerned with the following nonlinear Schr\"odinger equation $$-\varepsilon^2\Delta u+ V(x)u=|u|^{p-2}u,~u\in H^1(\R^N),$$ where $N\geq 3$, $2<p<\frac{2N}{N-2}$. For $\varepsilon$ small enough and a class of $V(x)$, we show the uniqueness of positive multi-bump solutions concentrating at $k$ different critical points of $V(x)$ under certain assumptions on asymptotic behavior of $V(x)$ and its first derivatives near those points. The degeneracy of critical points is allowed in this paper.

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Daomin Cao, Shuanglong Li, Peng Luo. 2015-04-23. Uniqueness of positive bound states with multi-bump for nonlinear Schr\"odinger equations. https://arxiv.org/abs/1504.06144

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