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

Given $\rho >0$, we consider the problem $$\text{find }(\lambda ,u)\in \mathbb{R}\times H_0^1(B)\text{ such that }\{\begin{array}{ll}-\mathrm{\Delta }u+\lambda u=\mathrm{\mid }u{\mathrm{\mid }}^{p-1}u& \text{in }B\\ {\int }_B{u}^{2}dx=\rho ,\end{array}$$ where $B$ is a ball in ${\mathbb{R}}^N$, $N\ge 1$, and $1<p<2^{\ast }-1$. Without any further restriction on $N$, $\rho$ and $p$, we prove the existence of infinitely many radial solutions, and, in dimension $N\ge 4$, of at least one non-radial solution.