Radial uniqueness and nondegeneracy for the Robin Lane-Emden equation

In this paper, we study positive radial solutions of $-Δu=u^p$ in a ball $B_R\subset\mathbb{R}^N$, subject to the Robin boundary condition $\partial_νu+βu=0$, where $N\ge2$ and $β>0$. For every Sobolev subcritical exponent $p>1$, we prove the existence of a unique positive radial solution and its no