We study the following nonlinear scalar field equation $$ -\Delta u=f(u)-\mu u, \quad u \in H^1(\mathbb{ R}^N) \quad \text{ with} \quad \|u\|^2_{ L^2(\mathbb{ R}^N)}=m. $$ Here $f\in C(\mathbb{ R},\mathbb{ R})$, $m>0$ is a given constant and $\mu\in\mathbb{ R}$ is a Lagrange multiplier. In a mass subcritical case but under general assumptions on the nonlinearity $f$, we show the existence of one nonradial solution for any $N\geq4$, and obtain multiple (sometimes infinitely many) nonradial solutions when $N=4$ or $N\geq6$. In particular, all these solutions are sign-changing.
Categories: math.AP