| Abstract: |
| We look for nonradial solutions of the following nonlinear scalar field equation
\begin{equation*}
%\label{eq}
\left\{
\begin{array}{ll}
-\Delta u = g(u),&\quad u\in H^1(\mathbb{R}^N),\; N\geq 3,\
%u\in H^1(\R^N)&%\quad\hbox{as }|x|\to\infty.
\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 $N\geq4$ minimizing the energy functional on the Pohozaev constraint. If in addition $N\neq 5$, then there are infinitely many nonradial solutions. 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. |
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