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

Abstract

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 $\epsilon$ 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.

References in corpus (1)

• Existence and local uniqueness of bubbling solutions for poly-harmonic equations with critical growth