Normalized solutions to the NLS equation in the ball for any prescribed mass

Nicola Soave

Given $\rho >0$, we consider the problem \[ \text{find $(\lambda ,u)\in \mathbb{R}\times H_0^1(B)$ such that } \begin{cases} -Δu+λu = |u|^{p-1}u & \text{in } B \\ \int_B u^2\,dx = ρ, \end{c…