Multiple nonradial solutions for a nonlinear elliptic radial problem: an improved result

We obtain an improved version of a recent result concerning the existence of nonnegative nonradial solutions $u\in D^{1,2}($\mathbb{R}$^{N})\cap L^{2}($\mathbb{R}$^{N},\left| x\right| ^{-\alpha }dx)$ to the equation $$-\mathrm{△}u+{\displaystyle \frac{A}{{\mid x\mid }^{\alpha }}u=f\left(u\right)\text{in }{\mathbb{R}}^N,N\ge 3,A,\alpha >0,}$$ where $f$ is a continuous nonlinearity satisfying $f\left(0\right)=0$.