  We prove new results concerning the nonlinear scalar field equation
\begin{equation*} \left\{ \begin{array}{ll} -\Delta u = g(u)&\quad \hbox{in
}\mathbb{R}^N,\; N\geq 3, u\in H^1(\mathbb{R}^N)& \end{array} \right.
\end{equation*} with a nonlinearity $g$ satisfying the general assumptions due
to Berestycki and Lions. In particular, we find at least one nonradial solution
for any $N\geq 4$ minimizing the energy functional on the Pohozaev constraint
in a subspace of $H^1(\mathbb{R}^N)$ consisting of nonradial functions. If in
addition $N\neq 5$, then there are infinitely many nonradial solutions. These
solutions are sign-changing. The results give a positive answer to a question
posed by Berestycki and Lions in [5,6]. Moreover, we build a critical point
theory on a topological manifold, which enables us to solve the above equation
as well as to treat new elliptic problems.
