Uniqueness of excited states to $-\Delta u+u-u^3=0$ in three dimensions

Alex Cohen, Zhenhao Li, Wilhelm Schlag

We prove the uniqueness of several excited states to the ODE $\ddot{y}(t)+\frac{2}{t}\dot{y}(t)+f(y(t))=0$, $y(0)=b$, and $\dot{y}(0)=0$ for the model nonlinearity $f(y) =…