Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations

Daomin Cao, Shuanglong Li, Peng Luo

We are concerned with the following nonlinear Schrödinger equation $$-{\epsilon }^2\Delta u+V(x)u=|u{|}^{p-2}u,u\in H^1({\mathbb{R}}^N),$$ where $N\ge 3$, $2<p<\frac{2N}{N-2}$. For $\epsilon$…