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

17 pages, 2 figures. arXiv admin note: text overlap with arXiv:1708.01228