Infinitely many nonradial solutions of a Euclidean scalar field equation (Q1310812)

In this interesting paper, the authors prove the existence of infinitely many non-radial solutions of certain problems \(\Delta u+ b(| x|,u)= f(| x|,u)\) on \(\mathbb{R}^ N\) where \(f\) is odd in \(u\) and either \(N=4\) or \(N\geq 6\). The key idea is to look for solutions with a very particular symmetry (with symmetry group a subgroup of \(O(N)\)). The proof is then by variational arguments.