Abstract
We prove new results concerning the nonlinear scalar field 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 ⩾ 4 minimizing the energy functional on the Pohozaev constraint in a subspace of consisting of nonradial functions. If in addition N ≠ 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 [, ]. 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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