On ground states for the L^2-critical boson star equation

Abstract

We consider ground state solutions $u\ge 0$ for the $L^2$-critical boson star equation $$ \sqrt{-Δ} \, u - \big (|x|^{-1} \ast |u|^2 \big) u = -u \quad {in $\R^3$}. $$ We prove analyticity and radial symmetry of $u$. In a previous version of this paper, we also stated uniqueness and nondegeneracy of ground states for the $L^2$-critical boson star equation in ${\mathbb{R}}^3$, but the arguments given there contained a gap. However, we refer to our recent preprint \cite{FraLe} in {\tt arXiv:1009.4042}, where we prove a general uniqueness and nondegeneracy result for ground states of nonlinear equations with fractional Laplacians in $d=1$ space dimension.

Replaced version; see also http://arxiv.org/abs/1009.4042

References in corpus (2)

• Uniqueness and Nondegeneracy of Ground States for $(-\Delta {)}^{s}Q+Q-Q^{\alpha +1}=0$ in $\mathbb{R}$
• Fractional dynamics of systems with long-range interaction

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• Infinitely many free or prescribed mass solutions for fractional Hartree equations and Pohozaev identities
• On-Site and Off-Site Bound States of the Discrete Nonlinear Schrödinger Equation and the Peierls-Nabarro Barrier
• Existence and stability of standing waves for nonlinear fractional Schrödinger equations with Hartree type nonlinearity