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

Abstract

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 \[ -\triangle u+\displaystyle\frac{A}{\left| x\right| ^{\alpha }}u=f\left( u\right) \quad \text{in }\mathbb{R}^{N},\quad N\geq 3,\quad A,\alpha >0, \] where $f$ is a continuous nonlinearity satisfying $f\left( 0\right) =0$.