Note on the multiplicity of solutions for nonlinear scalar field equations with a critical inverse-square potential

We are interested in the multiplicity of solutions to the following scalar field equation $$-\mathrm{\Delta }u-\frac{(N-2{)}^2}{4\mathrm{\mid }x{\mathrm{\mid }}^2}u=g(u),in{\mathbb{R}}^N\setminus \{0\}\mathrm{.}$$ We establish the existence of infinitely many radial and non-radial solutions.